I have told him, that i need some time to think about it and will get
back to him today.
To me, this implies you will get back within the day with either an acceptance or refusal. Therefore, if you didn't do this, and dragged the process on, I would immediately have doubts about you and whether I wanted you to join the company.
My plan is to call the first boss (far away) to send me the contract.
By all means review your contract, but bear in mind they will still want a response promptly - so it's unlikely you'll be allowed a few weeks to peruse at your leisure.
Given your situation, I would contact the second company and basically inform them of the first company's offer. Explain to them that you would prefer to work for them (it certainly sounds that way) and ask if there is any way to advance the interview process. If the company wants you enough, they'll do it. If they don't, they won't.
You need to decide how important/necessary the first job is to you. You've a firm offer already - is it worth rejecting this on the glimmer of hope a second company offers? I think your actions thus far are fine, but you've a short time window. Get in touch with the second company, determine what they're willing to do and if they don't get back to you take the job with the first company.
By all means ask to review the contract with the first company, but the longer you put off getting back to them, the more unprofessional it appears if you refuse them.
Of course, given their distant geographical location, you may not care about this - but I would never advise burning bridges with any company.
Be professional, be polite, be courteous and be sensible. Try and get a response on the second job offer, but don't forget you've a company who have shown you clear interest and are obviously keen to hear back from you - which sounds like a very promising start for a new role.