Welcome to the forum and sorry about the losses.
Completely normal. Really crappy first fish store too. Not sure how you cycled it those first three weeks but unless you had something in there that was adding ammonia, you weren't doing anything.
Prime is good, use that with every water change. You might also want to buy your own test kit. Liquid is better than strips. I, and a lot of others on here, use the API master kit.
Right now you are doing a fish-in cycle. Not the end of the world, but does require work on your part. What happens in an aquarium is bacteria grow that convert ammonia to nitrites to nitrates. Two different types of bacteria. You have enough of the first type to handle whatever fish you have now. It will take a little to grow enough of the second type that converts nitrites to nitrates. That's why I said about having your own test kit so you can tell if those get to lethal levels.
Nitrates will be present. That's why weekly water changes are needed to remove them.
Completely normal. Really crappy first fish store too. Not sure how you cycled it those first three weeks but unless you had something in there that was adding ammonia, you weren't doing anything.
Prime is good, use that with every water change. You might also want to buy your own test kit. Liquid is better than strips. I, and a lot of others on here, use the API master kit.
Right now you are doing a fish-in cycle. Not the end of the world, but does require work on your part. What happens in an aquarium is bacteria grow that convert ammonia to nitrites to nitrates. Two different types of bacteria. You have enough of the first type to handle whatever fish you have now. It will take a little to grow enough of the second type that converts nitrites to nitrates. That's why I said about having your own test kit so you can tell if those get to lethal levels.
Nitrates will be present. That's why weekly water changes are needed to remove them.