Upgrade button doesn't show once an infant is added. Just the way it is. You can upgrade...you just have to call for it.

No difference in waiting to add an infant, IME. For domestic tickets, no extra costs to add one, and they need a boarding pass and to be on the reservation, but don't require a ticket. Really doesn't matter if it's down at booking, over the phone sometime later, or at checkin. If you are upgrading (CPU or instrument), having an infant doesn't affect the process either way (except need to call vs. online for a cert).

As for seating, putting an infant on does block selection of the exit rows, but IME, doesn't block other seats that aren't available for lap infants. For example, A/B seats on CR2/CR7, can't be used if you have lap infants since there is only an extra oxygen mask on the C/D side, but you can select them online. Most agents don't check for this either IME, in fact, I don't think many even know where to look for the info. Typically, I'll hear an announcement at the gate (at least at CVG) before boarding for those with a lap infant to verify seating, but I've done it enough to know what seats I can/can't use on which UAX aircraft. So basically, much of this is done at the gate, even if you get seating with an agent, and on a full flight, there often needs to be shuffling. And on the E45, where there are only 4 rows are so where an infant can even sit.