I have to admit that the last point is the area I have the least experience in. In my day job I have experience as both a developer (not in game development mind) and some project management experience, but the last point is very specific to game development.
However, a technique I find that is always helpful when approaching my own projects is to start off with a high-level concept and start breaking it down. You want to start off with a particular image in your mind, and then start listing out the mechanics behind that concept. I remember watching a video with John Romero and Tom Hall doing a post-mortem of Doom, and Tom Hall briefly mentions his time working on Prey. He said he had this image of running up to a wall, looking up and throwing a grenade “up” the wall, with the gravity causing it to bounce up the wall and onto the ceiling.
Eventually you break it down into a set of discrete parameters (such as jump height, movement speed, fire-rate, damage per projectile, ammo count etc.) which you can then start tweaking based on feedback from testing. Initially you’ll try to use best estimates based on experience and your understanding of player psychology and then tweak from there.
I can’t recommend any books myself, but I’m sure others will have some recommendations of their own 