Hi ellen, welcome to the forum

We've all been there at some point. Shops are not the best places for advice, as you have found.
How many platies do you have now? And what's the male/female ratio? From your intro, I make it 8 in total with one, possibly 2 males.
It does seem odd that you haven't seen a very high reading for ammonia. The usual thing is for the ammonia to get very high, often off the top of the scale. Can I just check that you are adding reagents from both bottles for the ammonia test? I don't mean to insult you but it is worth checking every possibility

Brown algae is diatoms which are common in new tanks as the result of a lot of ammonia in the water, which is at odds with your readings.
8 platies is a lot for 38 litres, even 4 for the first few weeks is a lot for fish-in cycling and I would have expected higher ammonia and nitrite, though you say you have been doing drastic water changes which would have kept them low.
Clamped fins is a sign of stress. But as this fish is female, she could be about to give birth. Have you had any fry at all since you got the first platies? Though they might all have been eaten so perhaps I should ask, have you noticed any females suddenly looking thinner?
You mention having done a partial gravel clean - with that many fish that poo as much as platies do I would clean all the gravel every week. There will be some bacteria on the gravel but unless it is very deep, you shouldn't churn it up enough to bury all the bacteria in the top layers of gravel.
Washing the filter media (the stuff inside it) in tank water was the right thing to do. It's tapwater that can do damage to the bacteria colonies. As long as you aren't so rough that you dislodge the biofilm on the media, washing it is quite safe, and a good idea. The slimeyness on the surface of the media isn't biofilm, you can wash that off.
API stress zyme is supposed to break down sludge. But regular, thorough cleaning of that tank will do that too

So from here -
keep up the water changes and weekly gravel cleans.
Keep checking the ammonia and nitrite levels, and do a water change is you see a reading for either approaching 0.25. Once the readings stay at zero without having to do any water changes, you can start doing weekly water changes. With your stocking, I'd suggest around 30 to 35% a week.
Keep an eye on the platy you are concerned about. It could be she is about to drop fry or it could be a health issue. The calicos were the last ones in so she shouldn't have been through the worst of the cycle.
And regarding fry, don't try to save any. With 6 or 7 females in the tank each dropping a couple of dozen fry (probably more) every month, the fish population will get out of control if you try to save any.
I'll leave the plant question to someone else. After 18 years of fish keeping, it is only this year that have finally replaced all my fake plants with live ones, and easy live ones at that.