Paul;
 Welcome to the forum and good luck on your search for a Catalina 36. Certainly in the thirty six years since the boat was built, you can expect that a number of things have been replaced with new gear and the boat has changed.

First, let me answer you specific questions: Draft; Figure that the design spec's called for a draft of 4 feet 2 inches empty in salt water but that was a desgn spec and does not accuratly reflect what the final draft of the boat will be.  By the time you add the weight of 42 gallons of water @8.35 pounds per gallon and 30 gallons of diesel @7.3 pounds per gallon , plus all the pots pans, radios, and many pounds of misc. personal stuff, you be lucky to make the 4.5 foot draft ! Figure on a slightly less than 5 foot draft. Measure & weigh it during haul out survey. Many marine travel lifts have a built weight scale.

How much water ? Spec's on your 1988 boat called for 42 gallons. Originally there were two tanks in the aft cabin. One in the center line and one on the starboard side. The owner may have added a bow tank (not original equipment) at an additional 24 gallons.
 
Fuel; Many of the fuel tanks in that aged boat have been changed out. The new tanks are just slightly smaller to accomidate refitting in to the boat. The standard refitted tank is about 30 gallons with perhaps 27 gallons useable. (You never want the fuel to get down that low in a diesel tank anyway) There may be a plate on the tank specifing the capacity. 
On the dual buttons on the rail, there are several different style covers that fit over the teak rails, some that just fit over the teak cabin top rails and some that fit over the rails and the window. (Picture below)

What to check ? Everything ! Have a good survey of the boat (You'll need it for insurance anyway) Rudder, engine, etc. Figure you'll put 10% of the purchase price of the boat fixing her up to get what you want.
It might be an idea to mention your location and we'll know what types of conditions you're sailing in.
Search the forum/technical library here for the manual that came with your 1988 boat. Don't be afraid to ask questions here. We've all been where you are. 
You might some valuble pre-buy information in these articles by David Pasco; https://www.yachtsurvey.com/
Bill
 

Paul,
Quite possible I have that quanity wrong and yes it is possible, although I do not think there were optional tanks offered. Perhaps someone here on the Forum has a 1988 and the correct answer as to total capacity. . Did you research the tech section for the manual/spec sheet ? It also may be that the two tanks hold different quanities of water.
That refrigirant tank you pictured is filled with type 134a refrigerant and is probably for the refrig. If the boat had air conditioning there would be cold air vents located through out the boat.

Congradulations Paul !
How is she equipped ? Just curious as to your location ?
 Bill

Congrats on buying a great boat!  Mine is a '93, and it did come from the factory with 3 water tanks holding 80-ish gallons of water total.  At some point, Catalina added a 3rd water tank under the v-berth for the extra capacity.  My boat was also hit by lightning in 2014 (before I purchased it) and partially sank when the strike blew out the depth transducer.  Of course, all of the electronics, charger, and batteries had to be replaced, and it sounds like your electronics have already been done.  I also had to replace the water heater element, and the GFCI AC outlet at the chart table.  There are some devices that were ruined by the strike that I haven't replaced yet, such as the battery monitor and the AutoMAC alternator regulator.  Otherwise, everything else was OK.

I have had my '85 since 2005, and she has brought me much joy over the years.  Stay on top of the required engine maintenance, and she will give you years of happiness.