kaite - write, but it could also mean "scratch" or some other verbs. I reckon you mean "write".
oyoide - swim
hanashite - talk. But as above, could mean a couple of other things (for example, "release")
katte - buy, but could mean a few other things (for example, "win").
kaette - return, but could mean a few other things
tatte - stand, but could mean some other things
yonde - read, but could also mean "call"
asonde - play
This is why kanji is so important - if you write "katte", a Japanese person won't know if you mean 勝手、買って、勝って、or some other verbs. Anyway, I chose the most common words for what you wrote, but be aware that there are a lot of homonyms in Japanese.
"mase" is kind of an advanced level verb ending, so I wouldn't worry about it now. Its a polite verb ending that you say to someone who you wish to show deference to. Most often heard when you walk into a shop, and the clerk says "irasshaimase" (please come in) . Or, if the clerk asks you to wait, they might say "sukoshi o-machi kudasaimase" (please wait a bit). But its very much an intermediate or advanced level verb ending. I think it might be confusing if you are just getting into the shallow end of the Japanese pool.
