Fellow airheads, I am a new proud owner of a 1982 R65. This is my first motorcycle so I am not entirely sure what I am doing.

Here is a picture of the bike:

A quick description (from seller):
16000 Miles. Features upgraded Marzocchi shocks, beefy K100 Forks, 34mm Vikuni VM Carbs. Bike has been serviced including: top end refresh, valve adjustment, final drive service, carb sync, etc.

I got this bike from a little shop in DC. Owner said it has been sitting for a long time.

The current problems I am facing:

• I am leaking fuel from the right exhaust nut

• Tiny leaks at the oil pan

• The bike starts fairly easily with the Mikuni chokes in the DOWN position (CHOKE OFF), however, after letting idle, and then revving the engine, the bike shuts off (see video).
[flash=] https://www.youtube.com/watch?v=Cet85Zphamg [/flash]
• Bike shuts off when carb chokes are in UP position (CHOKE ON) and starts easier when carb chokes are OFF - a bit strange?

• The mixture screws were messed with, any advice on these Mikuni V34 Carbs?

My next steps are to:
Tuning
1) Valve adjustment following this guide:
https://www.motorcycleclassics.com/mc-how-to/adjust-valves-bmw-5-airhead-engines
If gaskets looks good, I will probably keep them.

2) Check/replace "$2000" O-ring where oil is leaking

3) Check/replace seals around exhaust nut

Minor Fixes
1) Fix right indicator light
2) Replace center stand spring

Questions:
Do you think I should go through all these tuning steps?
How can I fix some of these problems?
What are more good sources for information? Tuning equipment?
Is there anything I am missing? 

Tools/Equipment Needed:
Exhaust nut tool
Torque wrenches (in/ft sized)
Spark tester
Magnetic drain plug
Contact point set and condenser
Valve cover gasket

In other news:
I get my motorcycle license in two weeks.