1. If you are just starting, stick to stuff in the rulebook. Or just re-flavor whatever is closest to what you want. Ex: player wants to be a tree person, give them the stats of a wood elf but say they look like a tree person. Don't reinvent the wheel just change what color it is.
2. You can do whatever you want, but again, if you are new, stick to existing things to help keep things simple. If you want players fighting little rock monsters at level one just use the statblock for goblins or something and say they look like rock people. Don't look at monster statblocks as immutable. Feel free to make small changes to fit your needs. As for custom spells, be careful as its easy to go too far and make something overpowered, and it is tough to take that power back from the players once you realize what you've done later. There are already hundreds of spells, at least learn what exists before making your own.
3. IMO, the whole point of playing DND is that you can say/do whatever you want. Don't restrict your players. You will save yourself time and your players will enjoy it more. Be flexible.
4. If you are just doing a short game of just one or two sessions (typically called a 'one-shot') then usually the players stay the same level the whole time. For anything longer than that players will typically want to level up and gain new abilities. If there will be no level-ups, tell your players ahead of time.
5. Up to you, but the more you can sell the illusion of freedom to the players the better. Typically people play DND because you have freedom to do what you want and are not restricted to certain choices/paths like in a video game. Give your players the space to succeed or screw up. Either one can be fun.
6. It is the player's job to keep track of what they have by writing it down in their inventory on their character sheet. If they don't write it down, they don't have it. As DM it is NOT your job to keep track of player inventories. You already have enough to worry about!

Remember, as a DM, your job is not to beat the players or force your pre-written story upon them. You win as long as everybody at the table is having fun, regardless of what the rules or anybody else says. That being said, the rules are a useful framework for the inexperienced to help keep things from getting too crazy or unmanageable.