Hi Michelle,
Welcome to BP!
When you say "pull out" the equity, you're referring to a cash out refinance. With most banks and commercial lenders (backed byFannie Mae / Freddie Mac ) your max LTV (loan-to-value ratio) is 75%. IF you were to do the refinance you described above you'd only get $5000 cash out. (less the costs of obtaining the new financing)
Search BP for the "BRRR strategy". The goal is to purchase that property at 70% value LESS any repair costs (Buy), do the fixup (Rehab), get it Rented, hold for six months minimum and then Refinance at 75% LTV, which should give you all your money back out + 5%. At least that's the idea on paper. You should not get hit with capital gains unless you sell.
I'm less confident about my answers to your last paragraph, but here goes:
Everything is negotiable. Most of the time existing leases survive the ownership transition. If you don't like the tenant(s) you wait until their lease expires and then do not renew it. Gracefulness of exit varies :-) Deposits should get transferred from the previous owner to you during closing. Again, make sure to address this during purchase negotiations.