Hello and welcome! In Phoenix you can certainly grow plumeria. You're actually starting at the "end" of plumeria season, typically plumeria go dormant over the winter and you'll probably need to bring plants indoors when your temps dip below about 50 degrees. However, overwintering is a different subject! LOL!

If you have cuttings on the way I've been told that you are better off to try and root them than to keep them until spring, but maybe someone else has different advice. I would think you'd probably need a grow light / heat mat to root a cutting over the winter. They typically like to be around 85 degrees to root (they like bottom heat a lot), so you can see the cooler night temps are not enough. Plenty of people root over the winter, so although challenging, certainly not impossible! The same will go for your seeds.

I would definitely re-pot your HD purchase, the soil in those is usually WAY too peaty and moisture retentive.

Once cuttings are established, for the most part they branch after they bloom. After your plant pushes out the "inflo" typically you'll see the branch tip begin to divide. The number of tips will vary from plant to plant.

I hope this answers some of your questions, you're certainly in the right place for plumie advice, everyone here is great!