There are no obligatory exercises. Do what you feel working well for you. That having been said I know plenty of tall lifter than ended up being pretty decent bench pressers. I wouldn't call them skinny (they were when they started out) but their mechanics of long arms was certainly a disadvantage in the bench press.
From strictly a muscle-building perspective the DB press might be a better choice, but make sure not to cut your range of motion short just to handle more weight.
The floor press likely works well because It puts your humerus (upper arm) in a better pressing position, whereas because you have long arms and a thin chest, in a full range bench your humerus is pointed down too much, putting you in a very disadvantageous position.
First, you'll worry about an imbalance between push and pulls when you are not skinny anymore. Start by building the house before worrying if the wall paper of the kitchen blends in well with the color of the table!
Get as strong as you can in the basic movement patterns. Some will develop more easily than others, but right now it is not a problem. Worry about working hard overall and when you are of a much higher development level you'll work on balancing everything out.
When you are not yet good at pull-ups I recommend doing them every day at the beginning of each workout. Do not go to failure, maintain perfect technique and get 10 solid reps in however sets you require. When you can get 10 solid, non cheated reps in 2 sets or less increase the 20 reps... when you can get 20 in 3 sets or less move to 30. When you can get to 30 in 3 set or less start adding weight.
But focus on perfect form on every rep. Do not go to failure or even to the point where you need to compensate with other muscles or changes in body position.
Yes this Is quite comment I have written numerous times how the front squat is superior to the back squat with tall/long limbed people. There are no mandatory exercises, if the front squat feels better focus on that lift. Do the back squat from time to time to maintain that movement, but focus on the front squat to build your legs.
Everybody should train at a higher frequency on the big lifts in my opinion. My program design as far as training split is not different with aller individuals. We are all the same species, the main difference is in the selection of exercises.
I love Olympic lifts and have used them with athletes/clients of all physical types. But if you don't have access to a coach who can teach you properly I would probably stay away from them.
From a time investment/results ratio it is likely not a great choice, at least not at your level of development.
I wouldn't do a full arm day. But it is fine to do some direct arm work more frequently, you can easily do some work 3x per week at the end of workouts.
Also.... don't make generalizations that are too broad or inclusive. I've known plenty of tall, formerly skinny lifters who did not have the issues you mention. Stop seeing everything as if things will always be harder on you. You can't control that, just train hard and eat enough to fuel growth (taller lifters often need a greater caloric intake).
One of my friend was 6'3" and 171lbs. Pretty good on the deadlift because he had good levers but poor at benching and squatting. He didn't make much gains because he wanted to stay super lean. Only when he decided to eat for growth that he progressed... eventually he reached a 800lbs deadlift, 500lbs bench press, 700lbs squat and went as high as 320lbs. I DO NO recommend this approach, while at 230 he looked good when he went to 300 he wasn' that aesthetic. But the moral of the story is that when he decided to stop blaming his body type and just train hard on the big lifts and eating for serious growth he did progress.