Maybe there is no way to get explicit solutions for basket options (maybe the Black-Scholes differential equation can't be solved directly ??).
Q3: How do you price and hedge ( S1(T) + S2(T) - K )+ at time t. S1 evolves in $ S2 evolves in €, and the flows are in \$ ??
An alternative solution (if S1 and S2 were in $) might be Monte-Carlo simulation of S1 and S2 under risk-free hypothesis. The hedging is done using finite differiation method in the simulations.
Thank you already ;D