Welcome to the most addictive gardening there is. While I have been growing strictly heirlooms/open pollinated tomatoes, your questions are valid no matter the varieties.
1. To prune or not is one of those questions seemingly split down the middle. I do not prune other than to keep the bottom branches from touching the soil (in my case mulch). All soil has the potential to spread disease to the plants. As for the rest of the plant, I do not prune.
2. As for fruit, it depends a bit on the variety, the soil, the temperatures, the rainfall and watering. Mostly it depends on the varietal "days to maturity" range. Early season varieties will produce in 50-65 days from transplanting. Mid-season later and late season tomatoes even later. Most of what I grow are mid to late season varieties. I plant out about the same time as you and most of my tomatoes have small green fruits. Historically there will be ripe fruit the end of July or the first of August in my zone 5/6 garden.
3. Tie tomatoes up with any soft material. Tomatoes bruise very easily so stay away from rough material. These bruises and cuts to the stems are a perfect place for disease problems caused by stress to the plant. I would not use burlap twine. I use a 1/2 inch wide stretchy plastic tie that comes in a roll like tape. Cloth strips also do well.
Sorry this is so long but like I said, I like to share my addiction. Good luck.