Do crawl errors hurt my rankings?

A page that cannot be fetched cannot rank. Beyond that, nobody outside Google can promise a ranking outcome.

I have thousands of discovered, not indexed URLs. Am I penalised?

Almost certainly not. Look for parameter and duplicate addresses, and reduce them at the source.

Should I delete the pages Google will not index?

Not automatically. Merge thin pages into stronger ones or give them a reason to exist. Redirect an old address only when it has links or traffic and an equivalent replacement exists, because redirecting everything to the homepage just produces soft 404s.