1). In Recitation 11 we showed that Htm has a verifier, so that's mean Htm in NP and we know that NP in R , so Htm in R but Htm not in R.

I know that the verifier must be polynomial, so if the verifier for Htm did not accept in P(|(<M>,w)|) time so we reject so the verifier is polynomial ?????

what's wrong here?

2). When NTM gusses a string of lenght O(n) then run a verifier on it that the verifier runs in O(n) , why the running time for the NTM is O(n) and not O(n*(2^n)) (if we say that |Sigma|=2) since we have O(2^n) diffrent strings

so gussing a string will take O(2^n) ???