1 Yes the teacher will show you how to tune. After a few lessons, hopefully you can do it yourself. You have to tune every time you play.

2 You might or might not need the shoulder rest. I see some use it, some don't. Ask to try your teacher's shoulder rest, usually they have some spares. You definitely need rosin if you don't have it already. No rosin on bow, no sound will come out. Fortunately good quality rosins are relatively cheap, about 5-15 USD and it will last you forever. I'm using D'Addario Kaplan Artcraft and it's great. Pirastro Goldflex is also a popular choice. I don't think you need rosin more expensive than those two, as a beginner.

4 It will sound screeching in the first month or so, and your family/flatmate will hate you for it, I'm going through the same thing atm with my flatmate. Ultra Practice Mute is the answer, however you might not be able to hear your mistake, so practice without a mute if you can. To hell with those flatmates, they won't get a ticket to me playing Tchaikovsky at Carnegie Hall

I can see that you are very excited !! Keep that passion and excitement, you will need it when playing violin gets so difficult