"I played a lot yesterday."
You bring up a very important issue, namely when Kanji vs Hiragana characters are normally used. I thought Kanji would be for all content words, whereas Hiragana is used for function words and conjugations, but you correctly inform us that it is used for adjs & advs as well. Even if we are dying to rid our dependency on Hiragana, you caution us accordingly - thanks.
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.
My Japanese teacher said that unless you are a child, this generally means to spend time (hang out) with your friends. Per Jisho, there are several possible meaning including those you mentioned.
to play (games, sports); to enjoy oneself; to have a good time
to meet up (with friends); to hang out
The particle "wa" (which is written in hiragana with the irregular spelling は) is the topic marker, and it goes immediately after whatever you are marking as the topic.
In this sentence, "kinō", the word for "yesterday" is the topic. It's something like, "As for yesterday, I played a lot."
Your sentence is trying to make "takusan" the topic. It looks like it is trying to say something like, "Yesterday, as for a lot, I played," which doesn't make sense.
I think it's because they're in beta and only for mobile. They probably have a lot they want to add in the future. This language course literally just came out and involves an entirely new writing system so there's a lot of bugs that need to be fixed. Keep reporting the issues and eventually we'll help develop this into a much better course. :)
This is never explained by Duolingo. You have to stumble onto this fact whej you realise you're not learning effectively. And Duolingo will never say this as it will harm their marketing position. IMO, taking the time to interleave the 'why' before a lesson would help alleviate the stress for new learners.