I'm a second-career student who just graduated nursing school. Like you, I was scared stiff when I started. However, I actually did OK. Having worked in another career gave me perspective, and helped make me a better nurse. Being a bit older than the average nursing school student helped me be better grounded, and was an asset in dealing with adult patients. As a second bachelor's student I found my study skills were much improved the second time around.
Join the club. Nobody is very good at venipuncture in the beginning. It is a skill. As you practice it, you will improve. I am the clumsiest man on earth, and I managed to get certified in IV therapy. You can, too.
Sadly, you'll most likely have to start out working undesirable shifts. You will likely spend a significant number of holidays and weekends at work. If this represents a major issue for you, nursing may not be the optimal career choice.
Everybody worries about this, including me. Just keep your head in the game, be rigorous about the five rights of medication administration, and don't be afraid to ask for help. You'll do fine.
Statistically, the chances of catching a serious disease while working as a nurse are quite small. Even needle sticks rarely result in infection. I wouldn't worry too much about this.
This is a legitimate worry, but you'll be taught proper lifiting techniques. Just use them religiously and don't be afraid to ask for help when moving a patient. If your hospital has a lift team, make use of them.
Urine, feces, blood, vomit, pus and mucus are part of nursing. You'll encounter all of these things in nursing, although we sometimes exaggerate how often you'll have to deal with them. It can be disturbing at first, but you'll get used to it.
Most patients are decent people who are in the midst of the worst experience of their lives. In my limited experience, they generally respond well to even the smallest kindnesses.
On the contrary, most of us felt the same concerns and reservations before entering nursing school. I certainly did. But I made it and so can you. Nursing school is demanding, but as long as you stay focussed and keep your eye on the goal, you'll do fine. Best of luck!