The relevant link from meta stack overflow, the meta site which looks after the whole network, would be: Offering actual money as a bounty.
This was declined and there's some background here - Stack Overflow was originally formed because Jeff and Joel wanted to produce a site that gave excellent answers to programming problems, but not behind a paywall as experts exchange do. This has been the model since then.
The reputation system and badges are designed to provide incentives for users to both ask and answer quality questions. We have a high focus on quality, with rewards for editing and comments for peer review, so chances are in the normal course of using the system, you'll get your excellent answers. Have a look around - quite a lot has been covered already.
Creator brings up the possibility of bounties. These can be used when you're struggling to get an answer, as can the promotion link underneath any question.
In short, the normal use of the site does not require badges, or even (that much) reputation.
In terms of soliciting user contact, users have the option to provide contact details on their profile, should they wish to be contacted. Care should of course be taken here - you're effectively cold-calling.
In terms of on site contact for such things, answers and comments are not for that purpose. Answers soliciting off site contact will be removed, e.g:
Anyone have a solution? Please email firstname.lastname@example.org
As the idea is to make the valuable information available here, for free.