#2: It would be reasonable to take 20-30 days. I did it with a group in 28ish with a few rest days, if you are in really good shape (and the trail is!) you could do it in 15-18.
to answer #3: the LT basically starts in Williamstown. There is a short (3 mile?) trail that starts at the edge of town (very small town) and connects with the AT/LT at the Southern Terminus.
just looked up the Williamstown Approach in the GMC LT guide book. Pine Cobble Trail, 3.3 miles, 620 ft of elevation up the the LT Southern Terminus. Trailhead on Pine Cobble Road. I'm not sure where the bus/train would leave you in Williamstown, but it won't be more than a couple extra miles. I wouldn't be too concerned about adding a few extra miles to 270. The first shelter (if you are using them) is only 2.8 miles in from the Southern Terminus. 2.8 on the LT plus 3.3 on Pine Cobble, plus 2-3 in town is still going to be less than 10 miles for the day.