"I ran a lot last week."
You mean like after "last week" etc? As far as I'm aware you don't need to. Just a pause/comma works, that's how the Genki textbooks do it "週末、" I think it's more natural to not use は there as well, as I use HelloTalk a lot and I don't think I've ever seen any posts by native Japanese speakers that put は after.
From what I've seen, any relative time doesn't need は or に, such as 先週, 再来月, etc..
For specific times, you need either は or に, such as 午前九時, 六時, etc..
You can make a specific time relative with ごろ or 位 (ぐらい/くらい) like: 六時位, and then it doesn't require は or に.
For when to use は over に, its done to draw emphasis to the time. For instance, when you initially planned to meet someone at 2, but you're changing the plans to 3, you can emphasize that the new time is 3 with 三時は... However, it should be noted that this phrase doesn't tell the person you're talking to that the time changed, you're just emphasizing it so your partner knows you're aware of the change or to reinforce the time, like "I get off work at 5... make sure you pick me up at 5... i don't want to wait around after 5... please be here by 5."
Does anyone understand the difference between あまり and たくさん?
If you are interested, I developed a bit about this in the twin thread:
It's often hard to know with Duolingo. Probably the best thing to do is to work towards getting the kanji accepted by reporting it as another acceptable answer every time you see the kanji not accepted and eventually you'll get an email from them telling you that it's now accepted.