1) There is no limit to the amount of your available balance that you are permitted to convert.
2) If you have no other money in traditional IRAs, have $13,500 in basis and convert the entire $15,500 leaving you with $0 in traditional IRAs at the end of 2020, the nontaxable amount will be $13,500 and the taxable amount will be $2,000, determined on your 2020 Form 8606 and included in income on your 2020 tax return.
3) There is no statutory limit to the number of Roth conversions that you are permitted to do in a given period. The IRA custodian could have limitations specified in their IRA agreement, so you would want to check that. All of your transactions will be treated as if they occurred on December 31, so the actual timing of the transactions during the year does not matter.
