Regarding the summer, the yeshiva follows the traditional yeshiva schedule, where the “summer zman” is from Rosh Chodesh Iyyar until Tisha B’Av. There are 3 weeks off for bein hazmanim, and then back to the shtender for Elul Zman on Rosh Chodesh Elul.
A knapsack is like a soft backpack. No, it is not appropriate for a bochur learning by R’ Tzvi to be going around with a knapsack. Find a different way to schlep your things or leave them in your apartment.