mostly because it is getting cheaper, its light, easy and safe to handle, easy to clean and is easy to rejoin in an emergancy to get you winching again.
the suitability of the winch drum is governed by it being grooved to start the bottom layer of a wire rope or a flat drum, if you have a flat drum you're good to go. If its a drum with an in drum anchor for the winch cable you should crimp an aglet onto the end of the rope or an electrical crimp of the right size and cut the eye off of it. If its a side mount on the flange of the drum crimp on an electrical eyelet and you're good to go. in a pinch you can tie a timber hitch or choke hitch around the drum and just hold tension on it till it takes up tension on the recovery.
most likely the minimum guaranteed breaking strain you should use this number and punch it through basic rigging numbers to come up with the SWL when you're using it. best guess on a single line pull you should be good to pull about 3.5t(line pull not vehicle weight) while staying within all the safety margins.
most electric winches have the brake on the drive shaft from the motor. This uses the gearbox to increase the brake torque to the drum. These are the worst for heat on wind out. and if you do electric winch out often you should check it for its ability to hold load. Some other winches have the brake on the gearbox side of the drum inside the gearbox, these are spring applied and cam released. the only time these add heat to the drum is when the brakes ability to hold the load is exceeded and the brake slips. When this happens things get really hot really fast. In either setup, in most cases when you find out the brake wont hold you're not going to be worried about the rope, or the brake or anything else other than not being anywhere near whats unfolding followed by hoping that everyone else got as far away as you did.
no need for an eyelet in synthetic rope but you do want the eyelet to be big enough to comfortably feed a very large shackle pin through.
I like to set the eyes up so they are about 40-60cms long when finished, long enough to sit over the pully of a snatch block and keep the included angle at the splice under 45 degrees. such a large eye also makes it very easy to bend other ropes onto the eye when you want to join it and gives you an easy way of grabbing the rope when you need to haul it off the drum.

