Quote from docs for Dynamic:

continually evaluates f[val,expr] during interactive changing or editing of val.

which explains why your Dynamic is not touching w.

Dynamic[pp, {(pp = #; w = pp^2) &} ] is not interactively changed but automatically when you interactively change InputField content.

Following those points, your code should be rewritten to:

InputField[Dynamic[pp, {(pp = #; w = pp^2) &}]]
Dynamic[pp]
Dynamic[w]

Can I make it in such a way so that it will evaluate the stufftodo not in continuously monitoring manner but rather after (or while) I finished editing InputField[Dynamic[pp]] like the second argument options in Dynamics?