Can you use auto regen with Apocalypse's special regen power?

No, unfortunately.
Special powers that let a character use a power don't grant the power for the purposes of meeting feat prerequisites.

Nope. The true tragedy of Customs combining powers is that they don't meet the prereq for assigning feats. I guess it's the price you pay for 2 or more powers in one slot.

Same reason he won't work with Mental Shields and Compel. Being able to use an ability isn't the same as actually having the ability for prerequisite purposes.

Until they come out with feats that say something like:

Prerequisites: Regen or Special Powers that grant Regen

Then characters with Special Powers are a bit at of a hinderance. Granted they have Special Powers, but my Apocolypse would love Auto Regen.

I would say it should depend on the costing of the special power.

Does Regen+Invuln cost:

the same as regen,
same as invuln
the total of both
or somewhere in between either and both?

If it is anything but C and you assign feats that require regen and another for Invuln, you got a SWEET deal.

I assume the cost is somewhere between the cost of the higher of the powers and the total of the powers (if regen costs 8 and Invuln costs 10, then the SP costs 15 points) so you DO get a discount and that cost is frayed because:

a) you can have 2 outwitted in one shot and
b) you can't assign feats.

If its a custom fig, just give it regular regen.