Nitrate value is good for plants, won't negatively effect fish, nothing to worry about there.
Ammonia is at 2ppm, so if you do a 50% water change this should immediately bring it down to 1ppm. 50% minimum daily water changes until it's at 0ppm for a couple of days
. Don't clean the glass or remove any algae for a while, biofilm and algae will help stabilise the water conditions by consuming ammonia.
Also don't bother feeding the fish until ammonia is at 0ppm either, they will be fine for a week or longer if they were well fed before. More fish food = more ammonia.
I wouldn't bother with Seachem Stability, it's a waste of time for you. Studies show most "bacteria in a bottle" type of aquarium treatments have
very limited positive benefit when starting a tank from scratch (which your not doing), and not in the way the bottle describes. The bacteria on your filter and the plants are far more suitable than the bacteria in Stability. In your case it's just adding a tiny amount of waste into the tank with each dose IMO, so not helping, but probably negligible harm so don't worry.
Using Seachem Prime when changing the water should be enough, it will "detoxify" ammonia, but only in emergencies, it's not a long therm solution. If you use too much, it will actually inhibit bacterial growth, and I'm not sure what effect it has on plants when overdosing to detoxify ammonia. So use at normal dosages and just keep up daily water changes. If you see fish are distressed, just do a bight water change. You could even do one at the start of the day, and one at the end of the day. Whatever works for you, the more the better.
The floating plants should grow noticeably within the week and will help greatly by sucking up that ammonia directly. If you have your light on a timer, increase photoperiod to 12hours+ (more plant/algae growth = less ammonia).