Never managed to setup e-mail, I never get it to work. It requires so much, not really wagn's fault but getting past SPF checks and actually getting it to work with gmail and other options makes it very unstable.
Is there a way to add a User directly, give him a manual password which he can later change?
Yeah, when you invite someone. Whether the email gets out or not, they have a created account, so as admin you just change their password. IIRC, you go to their new user card, and navigate to Account->Details on the gear menu. Any admin can do this to reset any account pw manually at any time.
Same goes for requests, once you approve it, manually change it. Probably to a dummy one that you encourage the user to change themselves.