They have minor differences, and choosing 'again' for the translation on this question seems like an odd choice. "mata" is closer to "again" and "mo" is closer to "as well as".

So using "mata" it's more "let's do this activity again at -time-" (Today and then we'll meet again in two weeks)

and using "mo" is more "Let's do this activity at this time too" (We might meet next week, or tomorrow too but now we're extending our plans to two weeks from now as well)

I would like to know that as well.

Both should be accepted, reported that. また sounds more natural.

I wonder about this, too. In the past it really annoyed me how a non-literal translation that hat the correct context was not accepted. And here, the non-literal is the expected one. Please be at least consistent... I guess that's what I get for using a beta...

Since it's "practice again" I think も here means "as well" meaning "we'll practice next week as well (in addition to today/this time)"

No. を is an object marker, and since there is no object in the sentence, there is no need for it.

練習 can have an を particle after just like other する verbs but doesn't have to. Another example is 勉強. It can be written as 勉強をします but the を is often omitted.

Don't think so. It's just the way they have it. I've seen it in many other lessons done the same way.

Yes, しましょう is one word. It stems from します (to do). The "Xましょう" means "Let's X" in a quite direct way (where the listener isn't expected to decline).

Therefore, our sentence of 再来週も練習しましょう is quite direct, and it is fair to assume here that person A and B have already agreed to practice together again. This sentence might focus more on the fact that it's the week after next which is suggested. -> Today's practice was nice. Do you want to practice again sometime? -> Sure, let's practice again the week after next.

The more polite/indirect form of asking the question (in a way which allows the listener to decline) is the "Xませんか" form (literally "why not X"). So if you would rather ask the person if they wanna practice with you again, and allow them to politely decline, you would ask 再来週も練習しませんか = Why don't we practice again next week.

The reason duolingo split up your しましょう into し-ましょ-う is probably just to make things a bit harder for you ;) You would for example never see しましょ without the う, as far as I know.

Hope this helps ^_^

Actually that last う wasn't either -_-

I'm not that good at Japanese, but the way I understand も, it makes sense as it is. It doesn't go after the thing that is being repeated, but after the thing that is being changed.

Putting it after "practice" sounds to me like it would mean that you've already agreed to do X the week after next and you're suggesting practising as well as doing X.