In order:
1. Is this shotgun still gong to be useful today?
Yes. A shotgun is a shotgun even when it's an older model. It will serve just as well as a brand new current gun.
2. How do I remove the rust on this shotgun both externally and internally (see photos)?
I recommend getting some Kroil or CLP Breakfree and applying a heavy coat on the rusty areas.
Let soak a day or so to soften and loosen the rust, then apply more Kroil and "scrub" the rusty areas with a brass "toothbrush".
This will remove the rust without removing any bluing.
After a good scrubbing, wipe dry, and apply CLP Breakfree to prevent more rust, and to continue "working" on any hidden rust.
This will remove the rust but there will be pits and missing blue. Only a complete professional re-finish can "fix" that.
Some people recommend 0000 steel wool, but I found that often damaged the remaining blue. Brass won't, and the brush can be bought in any gun shop.
3. If there is rust on the outside can I assume there is rust on the inside in places that I can't see?
Not necessarily, but you should disassemble and look.
4. Is it possible to take this shotgun completely apart to clean it? How do I do this? Should I do this? And where can I find the manual?
You can field strip using the manual. There are no complete disassembly guides, but the field strip is usually enough. You can soak the trigger group in a can of paint thinner or use a "gun scrubber" spray to blast it clean.
After cleaning, lubricate.
If you don't feel comfortable doing this, any gunsmith can do it for you and give the gun a good, (and probably needed) clean and lube job).
Here's the manual:
stevespages.com/pdf/histandard_k200.pdf5. Where is the serial number located on the gun?
Many older guns do not have serial numbers.
Older guns were not required to have serial numbers until 1968 and many shotguns had no numbers.
6. What does "Proof Tested" mean?
It means that the gun was test fired at the factory with special proof loads to insure the gun was properly made.
7. What type of shotgun shells and shot should I run through this (if I am able to clean it correctly)?
Any 2 3/4" shells will work fine, but DO NOT use ANY steel shot. These older guns were made before steel shot, and steel will RUIN the barrel quickly.
You can shoot most any 2 3/4" loads of bird shot, buck shot, or slugs.
These High Standards were very well made guns, and some police departments used them.
They have a very good reputation.
8. Is "583.??" the serial number(see photos)?
"583.??" is the Sears/JC Higgins model number, not the serial number.
9. Is this gun exactly the same as the High Standard Model 200?
Yes, with possible minor exterior cosmetic changes to make the gun an exclusive for Sears.