Hey Nicolai.
1. I wouldn't train to failure every set. The bottom line is you quickly burn out if you do it for every set of every workout. That's why you hear people talk about training during their sets about 2 reps shy of failure. It's challenging, but you're not the point of absolute exhaustion. It would just, likely, make it harder to see progress, because your CNS is getting fried and you might have to take more days off or have more workouts where you're not even training near failure because you're so sore/tired. I would train to failure maybe for one exercise at the end of your workout as a finisher.
2. There's a lot of talk about this. Basically, from what I've seen, there's no significant impact. Any spike that might be caused is short and drops off quick, and any lowering of it normally bounces back as well. I might make a video on it.. but the main thing is it impacts your gains if it stops you from going to the gym.
3. I would probably need to see your form and know what your shoulder warm-up is to say what the problem is. If it's just during bench pressing, it sounds like a form issue. If it's general pain, it might be something you need to get checked by a massage therapist.