Firstly, how important is it to spend a lot of time remembering openings. I'm talking about my level here (around 1850 rapid, around 1700 FIDE rapid) and I'm not interested in playing fast time controls.
When I meet someone about 200 rating points above me in a slower time control, I need to know how to get into a decent position at least in the middle game. And pawn-breaks are my weakness, as well as surviving pawn-storms or avoiding them happening to me in the first place.
As someone of 60 years old who in my youth was playing for my school and my university but pretty much gave up for many years at the age of 22, do I have much chance of making any progress now? (I'm not looking to get a title but 1900 FIDE / 2100 sort of rapid on here rating would be nice, albeit I'd probably never get a game at a slower online time control with increment in that pool and probably face a lot of engine users)
Thanks for the extensive question. I still coach students about your age of which my dad is one. I don't know if there is any research on if someone can still make progress (win rating) after a certain age. I do believe that you can still learn new things and optimize your play, so that you can play towards your strenghts. If you do that, I'm sure you get an alltime high in your rating. For example, complicated dynamic chess as you get older is much harder as it takes up more energy and younger folks are just better at that.
Learning openings is of course useful, but only to a certain degree. Especially if you are older, I wouldn't aim for a detailed repertoire, but more one that speaks more generally and focusses on core positions and idea's.
What do you think is better for someone like me, computer analysis or self analysis of games
Both, use the computer to test your thoughts during the game. Computers are calculation beasts, so learn to analyse your games yourself from and with a coach instead. A coach can humanize what a computer means.