It depends if you are going to be using any battery zigbee devices (buttons, sensors, etc.). All Zigbee bulbs (Sengled is the exeption) try to be repeaters but they are very bad at it. So they would hurt your mesh if there on it. So if you have or plan on having any battery driven devices you are better of putting all bulbs on the Hue bridge mesh (be aware to put this on a different channel as your HE mesh (and check the frequency of your 2.4G wifi to stay away from that too)) and all repeaters and battery driven devices directly on the HE. That is the most stable way to go.
No, the two mesh's will be completely separate from each other... Also I don't know if the repeaters will work on the Hue bridge. If you have a problem with the range of the Hue Bridge you could either place a second bridge (creating a third mesh) or by placing more bulb between the ones out of range.
You (probably) don't need to. Hue bulbs are repeaters, so unless they're all extremely far away from each other or the Bridge, you likely won't need to do anything special. As stated above, this is a separate Zigbee network from Hubitat, and devices on one won't repeat for the other, but I don't think this specific point was clarified. To be extra clear about your other question as well, keeping bulbs on their own Zigbee network (Hue is fantastic for this, though some adventerous individuals have also experimented with a second, dedicated Hubitat hub) is better than mixing them with other Zigbee devices for reasons mentioned above as well.
And to be super-clear about a third point, the channel advice above is good, but keep in mind that Wi-Fi and Zigbee use separate channel numbers, so you'll have to compare the actual frequencies orlook at a graph to see how they line up. Also, keep in mind that you will often see Zigbee channel numbers in hex (if they're nice, this will be clear and start with "0x" or be indicated elsewhere) rather than decimal, so you may also need to convert there (e.g., 14 in hex or 0x14 = channel 20 in decimal). Hubitat shows you both, but I think third-party software like XCTU might just use hex.
Hue bulbs make wonderful repeaters for each other (and other ZLL bulbs). As long as you aren't trying to pass ZHA messages through your ZLL bulbs, you won't have any trouble with your mesh. This is why Hue can get away without having repeaters. The only devices that aren't repeaters are the couple of batter powered lamps they have. Everything else is mains powered and repeater.
In my opinion I would stick anything you want color animations with on Hue.
Hubitat had a hard time sending color commands as infrequent as every 5 seconds for me.
I'd love to remove hubs but I'd let Hue be the color slinger.