Ok. I had cheesecake too, so was a while!
Re. the attention, given your feelings and circs probably the best thing to try and do is up the quality of attention and live with the lack. So, if in an hour you can achieve 5-10 mins of really good contact that is better than 45 mins of half hearted attention.
Good attention includes;
Getting down to her level
Eye contact
Physical touch
Repeating back
Listening without speaking - letting her tell you but showing you are listening using eyes and touch and nods and smiles.
When communicating directly, mirror speech and ask questions that make her think, and try to reply with real comments rather than just 'mmm' and 'uh -huh'
Honestly, 5 mins of the above is so much more valuable than a day of placating so you can get on with other stuff, whether mumsnet or proper stuff like housework.
Secondly, try and tell her how you are feeling to some extent. This will help develop her budding empathy. Obviosuly I don't mean give her a guilt trip about your tiredness and grouchiness, but you could discuss feelings with each other. If you have been irrationally cross with her, it doesn't hurt to apologise here and there 'i'm sorry i was so cross with you but mummy is very tired and feeling grumpy today'. It doesn't necessarily undermine good discipline to correct oneself and also teaches about fallibility. (My second area to address!)
At a Parenting course I facilitated we used the weather to describe our week - and I've sometimes suggested using this with young children who can't communicate too well about how they feel due to age. Sometimes, they can imagine a dark rain cloud or bright sun as representative of their feelings better than being able to say I feel grumpy or I feel happy.
Now, as for what you say about seeing your DD as 'big' when DS was born, perhaps she did feel over burdened back then and maybe she does carry a bit of a sense of that now. It's not a big deal, but it's worth considering in terms of correcting her behaviour.
If she is feeling like the big older sister then she needs reassurrance and confidence building. It's quite scary being the eldest child. I am one and if you read a bit about birth order then you can sort of see how this affects thinking, even from a very early age. That's not to say one should try and correct the situation, but it is something to be mindful of.
The fork stabbing could be her 4 year old way of saying 'I may be the older, smarter, more capable child here but it doesn't mean I can't be silly and babyish and needing in guidance (so guide me instead of expecting me to lead the way here with that brother of mine)'.
Re. making mistakes - you can talk about decisions on a daily basis so that she sees that there isn't an automatic right or wrong always, and that we are all learning and choosing and making mistakes. Just little decisions like choosing a packet of biscuits (or whatever) at the Supermarket, for example. Make a choice on something together, sample the biscuits, talk about the taste and give your opinions. Thumbs up or down? This way she will become confident in assessing her own actions and choices, and see that she doesn't have to get it right first time.
This type of thing is a good indirect way of learning about judgement without having to overanalyse 'self' too much. Such small acts can have big impact on an experience hungry child. I'd steer clear of big talks such as 'now why did you do that nasty thing to your brother???' this will just instill a sense of 'badness'. Sure, correct the behaviour and explain about pain and unkindness but don't make it about her own self worth.
Can you see here where the weather and feelings stuff comes in? You are equipping her with the language and familiarity needed to consider feelings when you do that which further grounds any discussions about how people may feel when X, Y or Z happens.
Don't get hung up on this too much. It will be forgotten soon enough as your DD moves onto the next stage in her development, but I still believe it is worthwhile picking away a little at why she is chasing cats and poking her brother, if only to help her understand herself better.
My feeling is that although children have phases of this and that, and generally we pass them off as we eneter the next challenge with a 'phew! thank God the pooing on the carpet is behind us' attitude...we don't spend long enough thinking about why our children do the things they do, and addressing the underlying causes. I think the more ironing out you do now, the better equipped our children are as adults. Quirks are great but some quirks also give us big headaches as adults so it's worth going some way to acknowledging our children's behavioural idiosyncracies and at least slipping them a few tools for dealing with them in case they need those tools when they are 30 and dealing with their DHs and DWs and own children!