I bought a used CAAD10 frame and the bottom bracket seals were missing, presumably they fell off or stayed attached to the crank. Can I still use the bottom bracket? If not, I'll buy a new one and I have another question: I have a sram red quarq, do I need to use the sram bb or will any brand do?

No. Buy a new bottom bracket. They are cheap.

Get a new bottom bracket I say too. Every BB30 is the same so brand doesn't matter.

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The seals are not necessary, they just prevent dirt from getting into the bearings. So you should be able to use them.

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you can run without seals, but...

if you ride in wet weather, or dusty/dirty conditions, you will need to reduce time between servicing, strip, clean, regrease, or bearing life will be reduced

my experience is that not all bearings sold for bb30 are equal, i've had a set that were very slack on the axle, this caused fretting within just an hour, took them off, won't use them again

i never has this problem with sram branded bearings

Stick some tape over the ends!

If the seals on the bearings themselves are missing you need new bearings. But it's probably the secondary external seals that are missing. Those are less important. Unless you're riding off road or in the rain a lot you don't need them.

Few people regrease sealed bicycle bearings. Getting the seal off and back on without damaging it is a bit tricky on these small bearings with narrow seals. It's much easier on larger bearings with larger balls and thus larger seals.

The "seals", the bearing shields, are necessary in the sense that you need them to space the crank properly. You can also use some other method to keep it spaced.
Bike shops can sell you just the shields. If the bearings are at all questionable, just replace them.
as far as fretting, I've found that that is most often caused not by tight or loose fit, but by bearing misalignment. FSA makes a bearing alignment checker for bb30 that I wish was more available. the fretting is usually accompanied by marks on the spindle that are sinusoidal, indicating that the bearing is crooked.
Just my 2cents