If I am going to use a Kenwood TM-D710G for APRS, will I need to leave one of the VFOs on the APRS frequency of 144.390 MHz, or does the TM-D710G have a 3rd VFO built-in specifically for APRS use?
I don't own a D710 myself, but I was looking at buying one, so this is from my understanding of the manual: no, the D710 does not have a dedicated APRS VFO. If you look at page PACKET-2 of the D710 manual, it describes selecting which "band" (A or B) is used as the data band.
It only has two VFOs, band A and band B. You'll need to pick one of them for APRS. I have memory slots configured for APRS frequencies in the regions I visit (144.800 is APRS-EU, there is also 430.5125 on 70cm in the Netherlands I call APRS-NL).
Kenwood has a nice "APRS lock" feature. You can configure it to just lock PTT so you don't accidentally start transmitting voice on the APRS frequency, but you can also configure it to lock turning the TNC off accidentally or changing the frequency. I usually lock all three except when I'm in the Netherlands where I can often hear 70cm beter than 2m and switch between them.