Would the pronoun [nos] be in the same position in the sentence in European Portuguese?
In European Portuguese you'll probably hear "Elas veem-nos.".
Yes. Not probably, it's the only accepted form. At least in the Present Tense. If it were the Subjunctive, the pronoun comes before the verb (se / que / quando NOS vissem / vejam / virem). Mind the accent, by the way.
In Brazil can we also say "Elas veem nos" and still be understood?
You'll be understood, but it'll sound very weird, and it's not correct. "Elas nos veem" would sound too formal too. You'll most likely hear "elas veem a gente", actually.
I think most people learn languages to speak and listen, so teaching these arcane forms is wrong and pointless I think.
A verb book I have gives "vêem". Is the accent mark now obsolete?
Yes, it is no longer used when you have the same vowels together... veem, leem, creem, etc