I can't speak personally about adjusting the trigger. I know you can change it out for an aftermarket trigger if this is something you are thinking about.
As for best ammo for accuracy, as others always say here buy as mqny different types of ammo as possible and try them all.
I have perhaps 7 to 10 different brands of .22 ammo in the safe. F4om time to time I will do this in my pistols to see what is best. Honestly the federal bulk ammo seems to be just as accurate as the more expensive ammo I have. CCI Green Tag and some others. This is in my Mark II pistols.
I also have a 10-22 with Kidd trigger and barrel. It is accurate regardless of what brand of ammo.
No easy "adjustment" but there are a number of after-market parts made to improve the factory trigger, or as mentioned above, you can replace the whole trigger group.
Simplest is a replacement sear from Volquartsen or Power Custom.
I think there is also some guy over on rimfire central. If you send your whole trigger group to him he will lighten the pull. He will also upgrade you to a metal trigger guard if you pay for it of course.