i'm guessing the small tank you are talking about is the 15g? no, it doesn't hurt them if they get moved into a smaller tank and they will be ok. just don't put them in all at one because your tank has to cycle. you should either do a fishless cycle or only put in one or two platies and dont add anymore for a month or until the tank has cycled.
plastic is good but real is better. plants give the tank oxygen and use nitrate and ammonia for growth. however, with real plant you need some light so maybe not.
is the tank going to be near a source of light because you will need to have some light on the fish for atleast a biot of the day. to make day and night for them and so they can see the food and so on...
i hope this all helps. im quite new too, but it is quite easy to lear and you have this forum to fall back on if you have a problem!!! lol