10: Toroidal Tapa - the word 'additionally' is somewhat misleading because the solution doesn't have a continuous wall, you need to use the wrapping feature for it to be continuous

13: Can clue with 1|2 be changed to 2|1 ( 1->2 and 2->1) or to 2|3 (2->3 and 1->2) in both these cases 2 not lying about the value?

Yes. As long as you can represent a changed version where each digit goes one higher or one lower, it doesn't matter if they end up becoming digits that are already there.