Basel to Porto for non-EU citizen. Is there a passport check?

While I personally haven’t been to Porto, I would be very surprised if they didn’t separate Schengen from non-Schengen.

For all flights exiting the Schengen area, a check of identity must be performed. On the other hand, for flights remaining in the Schengen area, such a systematic check may not be performed by police or immigration officials. Thus, there must be a separate area for the extra-Schengen flights otherwise intra- and extra-Schengen passengers would mix with unforseen consequences.

Note that the above paragraph refers to passport checks by immigration officers. Both the carriers and the airport management may conduct security checks to verify your identity — typically, this means showing an identification document at check-in and maybe also at the security screening. They may choose which documents they accept, but given that the airline has accepted your non-EU driving licence (and also given that the airline is probably the lowest link, i.e. the one that will have to pay the others fines), I strongly assume that your non-EU driving licence will get you all the way.

Do note that while there are no checks, you should always have a passport (or other accepted form of ID — I think only relevant for non-Schengen EU citizens, though) on you in case of random police checks etc. You could run into problems by not having a passport with you. (But then again the same thing goes for Switzerland while your passport is lost.)

At BSL plenty of Schengen flights are departing/arriving to/from the non-Schengen sector, so you may well have to clear passport control there (without your passport being stamped).

If that happens, you're unlikely to get through without your passport and residence permit.