Lower Bounds for Frege and Extended Frege
1, 2, 4) The best known lower bounds on extended Frege are the same as for Frege: linear number of lines, and quadratic size. This applies e.g. to the tautologies $\neg^{2n}\top$ (basically, any tautology that is not a substitution instance of a shorter tautology, and whose sum of lengths of all subformulas is quadratic). This is proved in Krajíček’s Bounded arithmetic, propositional logic, and complexity theory for Frege systems, but the argument works for extended Frege systems as well.

3) It’s not entirely clear to me how exactly you define tree-like extended Frege (there has to be a mechanism allowing reuse of extension axioms), but I am not aware of any superlinear lower bounds on the number of lines in treelike Frege or extended Frege systems.