Regarding the bullet not sitting correctly on the seating die, yeah it can be a bit alarming at first. I started out loading revolver rounds where I had a definite flare on the case mouth and the bullets would sit there nice and straight as the case entered the seating die. When I started loading rifle rounds, my first experience was using some boattail bullets. They didn't sit on the mouth quite as steadily, but no big deal. When I finally tried some flat base bullets I was sure I was doing something wrong. The dang things would just fall right off the mouth and bounce around on the floor. I even thought about using my Universal Expander die to give them a slight flare, but didn't get that far.
It does kinda take a leap of faith to hold that bullet on top of the case mouth with your fingers as you guide it into the die, knowing that it will kind of tip over a bit before it makes contact with the seating stem. No worries though, they get aligned just fine.
It's important to note the distinctive "feel" that you get with each step in reloading. There is a way different feel when seating a boattail bullet into a case that has been chamfered and neck sized to where it is only 0.001" less than the bullet caliber as compared to seating a flat base bullet into a case that is sized 0.002" or 0.003" less than the bullet the way a few of my FL dies do it. Sometimes I do a double-take because the "feel" is so different from one combo to another. I have to double check everything to make sure that "feel" is not pointing to an error.