Shahar, the dimensions on that peel look pretty good (for NY style) but the top view doesn't show how well the peel is tapered. On bad peels, the peel is almost all flat, except for a small tapered area near the edge. On good peels, the taper begins at the handle and goes all the way to the blade, for a very thin very gradual point.
Here's a bad peelhttp://ecx.images-amazon.com/images/I/41ZTDx7C0OL._SL500_AA300_.jpg
For longer bakes, the broiler is less important, but as you shorten the bake time, the broiler is critical. In order for the heat from the broiler to have impact, the stone has to be located pretty high in the oven/towards the top shelf. The stone will pre-heat a bit faster on a lower shelf, but it will pre-heat to pretty much the same temperature on any shelf in the oven.
Plastic or glass proofing containers are better than bags. This is a good container:http://www.amazon.com/Pyrex-Storage-7-Cup-Round-Plastic/dp/B000LOWN3C
Get into the habit of taking photos of the dough after balling and after fermenting (get a photo of the bottom of the container)
Have you read up much on cold/refrigerated fermentation? That's how most of us are making NY style dough.
As far as convection goes, we're getting into a subjective area here. It depends on the oven, but, in my experience, convection gives you faster, more even browning. NY style pizzas are generally not very evenly browned. Shahar, up until now, I've been steering you, based upon your excitement regarding Mike's pizzas, not only into the NY style realm, but what I consider to be the best possible example of the genre. I'm pretty fanatical. If you've never actually tasted a NY style pizza, then you might want try some different approaches. You never know, you might like the results of convection. I would hope that eventually, once you get the right oven setup, that you will give my approach a try, but, until then, experiment with things like convection and other styles of pizza. There are many paths to pizza bliss
Matt, crushing tomatoes by hand is a last resort to get the driest sauce possible. I don't do it, because you do end up with lumps. Basically, tomatoes store water in their membranes, the more you break down the tomato, the more water is released. This is why tomato chunks will be less watery than puree, it's why you should never put tomatoes in a blender and it's also why, if you're processing them, don't go too far or they'll end up watery on you. Crushed tomatoes are generally preferable to puree- if you can get them skinless. I have a hard time finding crushed skinless tomatoes and opt for puree instead.