[SalesForce] Multiple Approval Processes for different Record Types

Nope.

Even from Apex code you (I'm simplifying a bit, full example here) you just call "Approval process engine, grab this record and have a look which approval flow it matches". It's a "first come, first served" thing - the order in which you've listed Approvals for given object and their entry criteria DOES matter.

You could submit it to multiple approvers at the same time and require them all to give it a go (search the help for "unanimous approval"). But that's still a limitation if you want multi-step approvals (everybody on level 1 would have to agree...).

Is this really what you want though - even if it would be possible opportunity would be locked until all requests have been approved/rejected...

You could try making your own approval process, it's not exactly rocket science. Make a small custom object in master-detail relationship to opportunity, call it "Approval Process" with field "Type" and submit these? Some cross-object workflow rule, rollup-summary field, trigger that would set a flag or simply a "Submit them all" button could take care of setting some hidden flag on Opportunity that says it's in middle of approval process... Furthermore (with more triggers) you could analyze who's current approver and whether you let him make changes to the Opportunity or not).

Yeah you're correct in that you can't use a User lookup field as the "Specify Initial Submitters" value.

However, there is a somewhat acceptable workaround. You specify that All Internal Users (or whatever is the most appropriate broad category) can submit the object for approval. But then you add criteria to the Initial Entry Criteria which says that the current user must be the same as Responsible__c ($User.Id = Responsible__c).

The downside is that when the user is not allowed to submit for approval, the error message they get is not user-friendly and doesn't say "You must be the Responsible User".

You can address the error message / initial submission flow with a bit more work by creating a custom button that uses the Approval API to submit for approval, and then you get the luxury of being able to give your users very customized messaging and up-front workflows upon approval submission, but that's quite a bit more work.