Is there a limit on how much I can convert from a Traditional IRA to a ROTH IRA in a tax year? Can I make an IRA contribution in the same tax year as I convert funds?

There’s no limit to the amount of the conversion but remember that you have to pay tax on that amount. Yes, the conversion does not count against your IRA contribution limit. 

No limit.   You can convert the entire IRA if you want to. 

Yes, the amount converted does not change the IRA contribution limits.