Woah boy on the voltage. Jesus, are you trying to flambe the pi or wot?
Sounds like you may need to beef up your ground and 5V wires between the jamma edge and the pi itself. For the best way yep, do your own micro-usb connector and don't power the pi from the GPIO (the usb port has a bit of voltage protection that the GPIO doesn't).
Switcher should be on about 5.25-5.30V maximum, giving you 4.98-5.00 at the pi.
Remember that not only does the pi naturally dip in voltage at bootup, but you have some additional stuff drawing power from the pi itself - usually just the jpac and the HDMI->VGA dongle. But if you have a USB sound card, that'll be taking some power too.
On my first build, I disconnected the 5v + gnd lines into the HDMI adaptor cable pcb and manually wired them to the jamma edge to save any strain on the pi itself. However since then I've found the laptop style dongles to be pretty efficient on power.
How is your audio amp wired up?
Finally on the warning icons, they can be disabled.. if you're confident no wiring is bad etc..
There is one for temperature, and another for power. The power one comes on by default if the voltage drops below 4.65V.
Add the following to your config.txt:
avoid_warnings=1 <- removes the warning icons
avoid_warnings=2 <- allows overclock / turbo even during low power or high temp
For the sync it's likely your monitor v-sync I'd say. Although the menus and loading screens run at 800x600 interlaced, so get into a game if you can first, and see how 320x240 is working before messing with monitor too much!
The jumpers on the JPAC are as standard from Ultimarc - I've never changed any of mine.
So that's the top and bottom jumpers labelled 31Khz and 15Khz with the jumper in place and the middle one labelled 25khz left open.
Sync-wise the jpac outputs pretty similar video to Pandoras Box, MVS, PGM and Taito-F3 mobos.
It is however pretty different to older hardware like Sega System 1 / 2 / 16, IREM, Technos pcbs and most bootlegs. So tweak your v-sync pot and see how you go, and only mess with h-sync as a last resort on the default dino monitor (it shouldn't really need any messing).