1. It’s hard tbh, and directly related to your second question. First of all, try to find out the reason Google penalized you and then only members here can suggest you accordingly. But overall, in most cases, as soon as Google penalizes, it’s better to leave the site and start over with another, unless that site is too valuable for your purpose of course.
2. Multiple aspects are involved in the vague “spam score” term. But assuming you are talking about the obvious backlinks, then the only thing you need to do is remove all the spammy links you are aware of and start building only quality editorial links gradually. Even if you can’t completely get rid of previous bad links, you can still build quality links hoping someday they will outperform the bad ones. The process is tedious and time-consuming, you've been warned.