1. yes, you can get unemployment benefits. If you paid enough tax to the state, that is your rights to get. Your problem for getting it will be you want go full-time MBA. How can you prove you are looking hard for a job if your status is full-time student?? Usually, it require you to show proof you are looking for jobs once or twice a month.

2. Not as I know of.

It doesn't matter you lay off at the beginning of the year. The time frame that counts are 12 months till the day you get laid off. hehe... you can't be denied for unemployment benefits because you get laid off at beginning of the year.