"I played a lot yesterday."
たくさん is normally written in kana only. Just because a word has a Kanji form doesn't mean you should use it in a sentence.
yeah, their meaning is pretty much opposite. takusan is a lot, (i ate a lot of cake), amari means rarely, almost not at all (i do not go to the gym often). also, usually amari comes in a negative sentence. hope that helps.
昨日はたくさん遊んだ We need more informal forms. Once you know the ます form, you can always build all the other formal forms ました、 ません、ませんでした but the informal forms are harder to remember. Duolingo mostly accepts informal forms as valid answer (when the context does not show if it is formal or not) but never provides them and to me they were not wet introduced. I think they are important to know.
Does this mean "I played around" or "I played some specific game"? Or should it be "I visited people"?