Investing in index funds as an EU temporary resident, possible? Are taxes only an issue upon withdrawal?

I want to invest through my wife’s name.

She is Russian which makes her options near zero now but is an EU temporary resident. Can she open an account and invest in index funds as a temporary resident?

This is a long hold retirement plan: are taxes only an issue when withdrawals happen and naturally heavily based upon where we are residents? (Say, capital gain tax in Dubai vs Germany)