CJ1234
To answer your first question about T/O performance, those airlines that do not use laptops do it exactly as you described. RTOW is calculated from the tables, then once you know the actual TOW you can get the engine derate (flex temperature) and the flap setting from the tables.
For safety reasons, sensible airlines will insist that both pilots calculate these figures independently, even to the point of insisting that the performance book is handed to the other pilot closed so he has to find the correct page himself.