Hidden trackable information in games sucks!
I play games for fun and pursuing the goal to win the game is fun! :)
1) Is it correct that a player can play spells regardless of which army card is chosen, i.e., a player does not have to choose/activate his planeswalker in order to play spells during the turn?
That is usually correct, yes - unless something else is stated in the spell description. Some spell description exclitly require target figures to be within X clear sight spaces of (or even adjacent to) another figure. (Clear sight spaces work slightly different than line of sight when attacking, see the clarifications on p. 13 of the rulebook.)
2) Is it correct that there is no line of sight requirement when playing a spell that affect a particular figure?