If professor x is feated with brilliant tactician with his in contact with cerebro can he target everyone he shares key word with anywhere on the map or does he have to choose a single fig as a focal point to count los from?

IN CONTACT WITH CEREBRO: If Professor X is in your starting area, he can draw lines of fire and count Range for his Speed, Attack, and Damage powers from the square of any friendly character with whom he shares a keyword.

Based on the wording, he can draw lines (plural) and count range from any character he shares a keyword with. Which would suggest he can choose different keyworded figures to draw his LOF for each use of perplex.

No, when he is determining line of fire he can choose one character. If that one character can see everyone then its fine.
Check Finap Word for more info.

I did not get that impression from the final word. While he must count range and LoF through a single character, nothing says he must continue using that character. Maybe my confusion is because of BT, but isn't each perplex a separate use, hence why you can modify different things?

No.
It allows him to modify multiple characters, it does not give him multiple perplexes.

its used to be a separate use each, that is why Strange was able to roll for each person, then they changed to saying it is one use.

Actually, it has always been 1 use, which is why that ruling never sat well with me.