For your concerns
1) welcome to lifting
2) this is the true sign of a conventional puller and frankly a badge of honor. It means you're keeping the bar close. Get higher socks if you want, but at a meet you wont be able to have them over your knees.
3) because conventional sucks and always sucks... just joking, kind of. Mostly because it's going to be a technique issue which leads me to:
What Rakshy said. You've got no external rotation this is going to put higher stress on your lower back/hips and make that pump even worse because it's not a true pump it's inflammation from improper movement patterns.
You're pulling technique is off a good bit, your hips are shooting up first, your lower back arch is collapsing-- all of which can be fixed with driving the knees out.
Practice the technique a lot at lower weight around 50-70% and really drive it in. Then eventually your deadlift will start to shoot up.
Good luck, I hate conventional