You are misunderstanding what the remainder is.

5 % 2 == 1, because 5 == 2 x 2 + 1

10 % 7 == 3, because 10 == 1 x 7 + 3

Your "edit 2" is mostly correct. I don't think of it "undoing" the division. But if that makes sense to you then I guess it's fine

It's not undoing the division, it never happens in the first place. Remainders aren't ever fractions, that's the whole point, they're left over because they can't be divided evenly. 5 % 2, you can take 2 away twice and you'll have 1 left over which can't have 2 taken away.

Wait, what?

Modulo is much easier to understand with clocks.

Suppose It is currently midnight. What time will it be in 3 hours? 3 mod 24 = 3. It will be 03:00

What time will it be in 27 hours? 27 mod 24 = 3. We go through a whole day (24 hours) to get back to midnight, then continue another 3 hours, for a total of 27. The time will be 03:00.

What time will it be 48 hours from now? 48 mod 24 = 0. 48 hours from midnight will be midnight.

What time will it be 6 hours from now? 6 mod 24 = 6.

Conceptually, X mod Y means that instead of 24 hours per day, we are splitting the day into Y "hours", labeled 0 to Y-1. We start at 0, and pass through X "hours". X mod Y is the "hour" we finish up in at the end. 5 mod 2 means we have a 2-hour day, with hours 0 and 1. We pass through 5 of those hours. When we finish, are we at hour 0 or hour 1?