There should be very minimal side play, 3/16 is way too much. You will need a flywheel puller to remove the flywheel. You can use an impact wrench to remove the nut. You can also put the bike in gear and lock the rear wheel to hold the flywheel while you are removing the nut.
I can't remember which stud is the oiling stud. It is either the top right or bottom right side stud. The oil should come out immediately when you crack the nut. If it doesn't you have a problem.
If I remember correctly the oil pump can be replace by removing the right side clutch cover and clutch assembly. Check out the Service Honda link on the left side of the page for a good parts source. They also offer a discount. OEM parts are best IMO.
Clymer manuals are ok. Factory manuals are best.
Can't recommend a shop in SJ but I can refer you to a great machinist in Petaluma if you need any machine work done.
Not sure how mechanical minded you are but, if it were my bike, I would purchase a good manual and then remove the engine from the frame and tear it down. They are not that hard to work on and you can send your cylinder head and cylinder to my guy in Petaluma and he can rebuild them for you. You probably have excessivly worn main bearings causing the side to side clearance and most likely a cooked camshaft and rocker arms due to the lack of oil to the top end. Check out
www.Edco.com in Petaluma for your machine work.
Sorry, that edco link does not work. I'll try to find a link that works.