Welcome whatsthegame! Plenty of room in the MN pool.
I came to swimming as an injured runner so started small. I couldn't even really swim very well.
I started off going 3 times a week for about 40 mins each time. I did the same routine each time (mentally, that worked for me) and slowly saw the improvement.
Now I go twice a week and do 1K front crawl in 25 mins. It took me about a year to build up to that and to learn to do bilateral breathing.
If swimming is your only exercise I'd say you should go three times a week for at least 1/2hr. I think it's better to go more frequently for shorter duration than just one big, long session, though obv that depends on the time you have available.
I can't comment on the eating cos I'm crap at that. Also can't comment on slimming down (already am slim). I do swim late.
What it has done though is really, really tone my arms up. They are not broad at all. If you're using more calories exercising than you're eating then you will lose weight. It's no impact so that's great.
The mental space it gives me is amazing.