If I have existing decking with old tar paper that I want to remove the tar paper and install synthetic underlayment, do I need to remove all existing cap nails in addition to the tar paper or can I leave the cap nails if none are protruding? There are literally a thousand cap nails in place. thanks in advance for advice
That's between you and your roofing manufacturer. The new underlayment may be more likely to wear through on the protruding caps, nuking your warranty. (Plastic caps are always protruding somewhat.)
I'd hire a couple teenagers to pull them. With a cat's paw nail puller it shouldn't take long. Many re-roof jobs I've done have required several thousand roofing nails being pulled individually as well.