#1
Does it matter what kind of capacitors I use for a pedal, as long as they still read the same?

I have a bunch of tantalum capacitors, and a few mylar.

And one last question, if it asks for tantalum capacitors, and I use mylar, does it matter?
DEAD. AIR. SPACE.

Fender American Strat/Tele->Vox V847 Wah->EH LPB-1->BK Butler Tube Driver->Big Muff Pi->MXR Carbon Copy->EH Small Clone->Vox AC30/Orange Tiny Terror/Blues Deluxe RI
#2
They will sound different. Some caps sound much smoother than others. Some caps add colorful overtones. Some are very transperant and don't change your tone while others will color your tone a lot. It's not just about the type of cap but different brands of the same type of cap will still sound different.

They if the values are the same then different types of caps (except for electrolytics) are interchangable so it's fine to swap them around and see what you think sounds best.
Not taking any online orders.