You are allowed to deduct mortgage interest on your main home (where you live most of the time) and on one second home, up to a combined limit of $750,000. The calculation shown in IRS publication 936 Table 1 aggregates your interest without regard to priority or interest rate. In other words, your method 1, more or less.
There are three methods to determine your average balance for the year. The easier one is to take the average of the first and last month mortgage balance. Suppose the mortgage on home 1 is $500K on January 1 and $490K on December 31, and the mortgage on home 2 is $400K when you buy the home and $395K on December 31. Your average balance is $892.5K so your deductible interest percentage is 0.840 (84%, rounded to three significant digits). There is a second method which is harder to explain that uses your interest payments to figure out the deductible percentage. The third method is to figure your average mortgage balance for the year by taking the average from all 12 monthly statements for both mortgages. This is what you will want to do for 2022, since your balance for more than half the year is well under $750,000 (since you have not bought the second home yet).
What you ask in #2 is can you prioritize one house over the other. I don't believe you can do that, there is nothing in the instructions that suggests it. I tried to find it in the actual law but I couldn't one way or the other. The instructions aggregate your interest without regard to your preference in deducting one or the other.
