Problem 1 is hell, most boring part of the game with a huge margin, nothing to do with it.
Problem 2 is also bad, but at least you can use the spare time to pick up the B1 Rations you need for later
Problem 3 is solved by going to floor 4 and freezing the key right after you get the hang-glider, and then use the elevator in the womans bathroom as a shortcut to get back to the tower building and fight UltraBOX. This means you don't have to backtrack after you use the hang-glider, and saves a lot of time.
I'll refer to this post I made on Gamefaqs about what items are needed for a non-TAS speedrun.
This list is made with the no-kills Big Boss ranking in mind (on the PS2 version), so depending on what level of stealth you settle on you could just punch guards to death rather than pick up those rations listed above.
Yes you do have to do that, and you can't skip the conversation with dr Petrovich either, or Running man won't show up.