the X6 is fine for a 4s pack. Pick up one that is above 5000mah. I have a ProMatch Racing 6500mah and it finishes a 15 minute run with juice to spare.

For eBuggy, a 1900kv motor is the norm. If you have a monster track, large straights, etc, then consider a 2000kv, but 1900 is the norm.

As for motor limits, not really. Ask your local track just in case.

If you will race at any ROAR sanctioned events, I believe 4S is max battery allowed, but for regular club racing, not uncommon to see 1400KV motors on 6S to improve efficiency and reduce temps. I have grown to rely on HobbyWing electronics and have only ran my buggies on 4S. I would consider investing in a parallel board too, might come in handy to charge 2 (or more) packs at the same time.

I have ran 2200KV motors in the past and would ultimately have to dial back the EPA anyway, also found that too high of a KV motor would be more likely for a front tire to become unglued... far less stressful for me running a 1900KV to 2000KV motor. Bumping up a little timing/boost on 1900K for a larger track is more effective IMO. I have also ran Deans compatible connectors for many years, but I do agree that Deans style connectors need to be replaced more frequently, I typically install a fresh set of connectors each time I replace the battery packs, I would go through a pair of packs every six months to a year.

In contrast, I have had problems with Deans on my 2S powered 4WD SCT, because 2S is less efficient it will push nearly double the current than you would typically see from a 4S setup, after switching to inline bullets my wiring issues went away on my 4WD SCT

A power supply will not charge a battery, rather it enables you to use it to power your charger, it (your charger) in turn will be more than capable of charging your batteries.

Assuming the X6 can handle 24V input I would use a 24V power supply. The charger will run cooler because it isn't having to boost the voltage, I do this with my 308. I run a 2600KV in my EB48, can always turn it down but can't turn it up. Of course track size plays into this.

some chargers have input voltage ratings that vary from 12V-24V and you'll want to read the fine print, for example the charger may say it can charge a 4S pack at 20A but that might only be possible with a 24V supply .... if you use a 12V supply then the charger may max out at only 10A as an example.

seems we go through this in various threads but I guess unless there is a sticky, the older discussions are harder to find. here are the Specs on the X6

Maximum Charge Power 800W
Charge Current Range 0.05-30A
Discharge Current Range 0.05-30A
Input Voltage 7-32V DC
Input Current 35A
LiPo/LiIo/LiFe 1-6S

Bottom line is the X6 will run OK on 12V and charge batteries up to 6S even though though those are over 25V fully charged. However, you will not get the rated power of 800Watts. This means you will not get the full rated current into 6S or even 4S batteries.

The key to understanding this in the Input current limit of 35 amps. Power is always volts times amps P=I*V and I=P/V
At 12 Volts and maximum input current, the available power is roughly 12V*35 amps= 420 watts or only about half the rated power.
At 6S, V=25 volts so 400watts/25 volts= 16 amps so a lot less than the rated 30 amps of charging current
At 4S, V=16volts so 400W/16V=25 amps so still not he full 30 amps but close.

So with a 12V supply you are getting close to the full potential into 4S batteries. 25 amps into a 4S 5000 mAh battery would be 5C which is too high anyway for a single battery. I know some guys charge at high rates to warm their packs but 2-3C is a safer charge rate. So 10-15amps for a single 5000 mAh pack. If you get into parallel charging, you could do 2 batteries at 12.5 amps each

If you want to get the full potential out of your X6, you need at least a 24 volt 800-1000 Watt power supply. 800W/24V=33.3 amps which is less than the 35amps max input current.