As far as (4) is concerned the English word "any" is ambiguous. I could see interpreting this as "If every subsequence... " in which case it is true. I could also see interpreting it as "if some subsequenc ..." in which case it is false.
For (5), I don't know what "Uconjugate" means. Did you mean U complement? In that case it is certainly not true! Or did you mean "Uclosure"? In that case it is true.