Hello everyone. I'm taking the chance now to read everyone's replies carefully. It's weird, when you're reading someone else's thread it's very interesting/ easy to read through lots of replies. But because this is my thread it's very difficult, I'm trying to wrap my head around each new idea and it's hard to respond to everyone/ think through every idea properly. There is some very confronting information here that has triggered a lot of thought, emotion, and reflection for me. But I truly appreciate everyone's contributions, whether or not the topic gets derailed at times 
. Though at the same time this is TOTALLY normalising this gay porn issue in my mind - no-one's fault, but when you're thinking about it so much and coming back here to read replies that discuss the issue so frankly, etc., you become desensitised to it and it starts seeming normal/ a non-issue! Like things will now have to step up a notch for me to feel like there's an issue.
I am thinking that for now, I will let things lie. If my dad is sloppy about using it again, I will casually comment on "the weird computer where there are always links to/ searches for gay porn. Does anyone know why this might be? Do we need to have it checked?" I think that is within my rights because it is a communal computer. Believe it or not, before this thread, casually mentioning the topic did not even occur to me as an option - to me the options seemed to be, stay quiet, or initiate an awkward direct conversation about it. This way I am making it clear that it's obvious, giving him the opportunity to be more discreet, and giving my mum the opportunity to know.
My sibling said to me this morning, "I've been thinking - do you think he WANTS us to notice and say something, so that he can "come out"?" This is another possibility that had not occurred to me before this thread, and it may be true - he seems very unhappy, someone who does so little each day and puts so little energy into life is probably depressed/ unhappy. It is hard when their behaviour then affects you and YOU become unhappy - but I need to focus on building some empathy for him here. It is also hard with him because when you let down your guard and try to be nice/ help him to feel happier, he'll take advantage of it, asking you to do extra things for him, etc., that you don't want to do.
I think I do need to step back, detach from the home dynamic by moving out. My partner is starting a new job with a significant pay rise, once he has settled in we can look at changing my living circumstances. At the end of this year my financial options will be massively better and I can be truly free from the atmosphere at home. It is true that at the moment I am prioritising completing my studies over leaving the home, which is what people in my "real life" keep advising me to do because then I will be completely free sooner, rather than in a prolonged semi-independent state (not studying fast enough, not earning enough). The course is very full-on so the part-timers feel like they're almost full-timers even though technically they shouldn't be.
The atmosphere at home is because we have all learnt that criticising anything, voicing disappointment or asking for help will be met with shouting, insults, threats, etc. We all therefore have just given up and get on with things ourselves rather than involving him or asking him to help more or behave in a considerate way. It is less aversive to clean up after him, just accept the situation, etc., than it is to trigger one of his "rages". I don't think that's a healthy dynamic but it suits him! On the other hand, as I mentioned in a PM that I sent to someone, he is not a one-dimensional caricature - he does kind things as well, he can speak kindly, etc.
As I also said in a PM, regarding whether or not my mum has seen the gay porn when he's slow in minimising the screen - I suspect not, simply because she tends to spend her time in different areas of the house, and if she suspects nothing and isn't familiar with computers, she mightn't read any meaning into windows closing or rapid clicking when she approaches/ passes the room (I'm sure you know what I mean). She also mightn't think to look sideways because she doesn't suspect anything and would be passing on her way to another room. BUT it is also possible that she has seen it and doesn't care.
Regarding using analogies to make a point (i.e., cigarettes) - I have always felt analogies can be used to support any point. e.g., if in an analogy I shifted the "severity" of the issue up a notch instead of down - for instance, maybe on top of everything else, finding love letters between my dad and another man like mathanxiety's daughter, or even coming home unexpectedly one day and finding my dad with another man in the house - then I think that would persuade people towards the "tell your mum" perspective, even though it's the same notion of coming across something "secret" that's relevant to your parents' relationship, not you.
Another thing I am going to do is resolve to be there more for my mum. At the moment I tend to cope by spending as much time out of the house as possible - which means I don't see much of my mum, as well as my dad. If I spend more time with her that might help her/ strengthen our relationship and I can get more of an idea of what she might think and want.
My dad isn't the main breadwinner - I think my mum actually paid for the computer in question! She pays for most large purchases. She also paid off the house I believe - before she met my dad. I know that that's kind of irrelevant - in a family assets are usually pooled - but I thought I'd throw that in there because there does seem to be an assumption that my dad is the "big financial contributor" and this somehow affects his position in all this. I don't agree with the idea that "he is entitled to behave however he likes and if people don't like it (including my mum) they can leave". As in, I don't think he's the central figure in the family that everyone should revolve around.
Incidentally, on a more intellectual/ irrelevant level - as part of my paid work I have visited a number of domestic violence organisations and interviewed the senior staff there, and I understand what MakeYerOwnDamnDinner is saying. The managers of these organisations have all emphasised the critical importance of adopting a feminist perspective. MakeYerOwnDamnDinner said, "The cause of any sort of domestic abuse is the desire on the part of the perpetrator to control and dominate his partner and family and his underlying belief that he is entitled to do so". My understanding is that all the other factors discussed here may contribute - but people can experience those factors without becoming abusers. The key, causal factor for becoming an abuser is "the desire on the part of the perpetrator to control and dominate his partner and family and his underlying belief that he is entitled to do so" - without that you would not become an abuser no matter what your circumstances. I hope I understand that correctly.
mathanxiety, thanks for all your excellent and confronting/ thought-provoking links. I will definitely be reading more of them, trying to get a hold of books, etc.
MrsFlittersnoop - thank you and I feel very sad for your sister-in-law.
antsypants - thank you though I'm not sure I understand your point of view. I'm writing a lot here because I'm trying to ensure that people have an accurate understanding of the situation, so that their advice is maximally relevant/ helpful, and also to answer people's questions if they're about central issues that will affect their advice. I am hesitant to just blurt everything all out to my mother because when I started the thread I wasn't sure whether it was even my business to do so and it could create chaos that I might really regret, I don't want to act rashly. As I've mentioned previously, I have friends who have been in really bad family situations, and a parent initiated a split, and then really regretted that split further down the line. However dysfunctional the family is, I also don't like the idea of setting something into motion that causes it to fall apart (although I appreciate others' advice that it is not MY behaviour that could result in that, so I'm not "responsible" in that way). I guess that's why his threats to leave are effective in shutting people up! I really don't think my motives are any deeper than that.
anokhi - fantastic post, thank you. :)
ItsGraceAgain - thanks, good to hear from someone who has been in a similar situation. No, I can't afford a detective!
holyShmoley - good point, that's how I feel.
thisisyesterday - haha! (Re: your first sentence). Thanks for your advice.
perfumeditsawonderfullife - thanks for your very good advice, it seems your moral compass is similar to my own.
Caterpillar2Butterfly and PaulaYates - thanks, message taken on.
It seems like the tide of this discussion has turned, with most people saying that it is most "right" to tell my mother in some way, and I think the way I suggested above is a way in which I can make sure she knows the facts without intruding too much on their relationship or feeling too uncomfortable or creating huge conflict.
I do think some of the arguing on this thread is probably like arguing about which religion is right/ whether or not there is a God - i.e., it will go on and on and no-one's viewpoint is going to change, and people will just feel more vindicated in their beliefs.
I am going to take mathanxiety's advice and not visit this thread every day if that's OK, because I'd like "gay porn" to take up less of my days!