First off, i'm not going to preach on feeding live or frozen, but there are major benifits to feeding frozen as opposed to feeding live. The first is the saftey of the snake. If your BRB is not hungry, it will not eat, period. If a live mouse is left in it's enclosure for too long or not monitored, it could very well kill your boa. Also, even when the boa attacks and constricts the mouse, it is possible for the mouse to bite and scratch, injuring the snake. Second, rodents can carry bacteria and internal parasites, which if you feed to your snake, will be passed on. Freezing rodents for 30 days will kill most if not all these parasites, making it safe for your snake...Third, you can keep plenty of frozen mice on hand as opposed to having to continually go and buy them or raise them yourself (smelly!)...Also, please make sure that the prey item is COMPLETELY THAWED! Feeding a frozen or partially frozen food item to a snake or any reptile for that matter can be fatal. I said i wouldn't preach about feeding frozen, but i guess i ended up doing it...oh well, it needs to be said.
On to your next question. It is advisable to wait at least 2 days after feeding to handle your snake. Otherwise regurgitation due to stress can occur. This can be especially devastating since you have a juvenile snake.
If your snake doesn't respond to just leaving the mouse in it's tank, use the tongs and shake the thawed mouse in front of it, just like a live one. This can sometimes incite a snake to feed when it normally wouldn't. If it doesn't feed, don't bat the snake around with the mouse in the head, just throw out the mouse (it's generally not advisable to re-freeze thawed food items) and try a few days later. Hope this helps.