Welcome to the forum!
Any clutch from a Liberty twin will work fine, but there are wide roller clutches and narrow roller clutches; the wide roller ones are stronger.
It's water cooled.
There is an electric start kit available. Finding one may be a problem... best bet is to look at a used snowmobile yard. One such place is
Al's Snowmobile Parts Warehouse - Snowmobile Parts, Snowmobile Parts, and More Snowmobile Parts. You will also need to replace the primary with one that has the machining for a ring gear to allow the starter to turn the primary.
The biggest problem with the 800 is in the crank. There have been a lot of broken ones, especially out west in the mountain sleds. The issue is the torque the engine produces; it hammers on the crankcase and eventually wallows out the PTO end of the crankcase until it can't support the crank. Then the crank breaks. Keeping the clutch balanced helps this issue. Some guys have had good luck going to a wider PTO end bearing, it spreads the force across a greater area in the crank. Some guys replace the crank every couple years and make sure their case is line-bored to keep it exact. Adding an engine plate, torque link, and push stop are also things that can be done to keep the engine going. The VES valves are aluminum and have had issues; there is very little cooling in the cylinder area around the guillotine. The guillotine can melt, and can destroy that piston/cylinder. Going to stainless steel guillotine valves solves the melting problem. Stock HP was about 136-138, but with an SLP pipe/can and adding a few flowrites and aftermarket reeds, you can bump that easily to around 150. Compression on mine with new rings/pistons was 150 psi.
Be careful with jetting changes, there is a mid-range lean condition that was addressed in 2003, if you use the 2003 spec, you will burn the engine down. 2002 had it's own jetting chart and it's a LOT richer on the main jet than later years.
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2007 RMK 700 155", 2008 RMK 600 155", 2006 RMK 600 144", 95 Prowler 550 2-up, 1990 Indy 650
RIP, destroyed by fire 1-22-2008

04 RMK 800, 05 RMK 600, 02 RMK 800, 97 RMK 700
http://www.avalanche.org/accidents.php