Responding to your queries below:
1. Incorrect. The scholarships could go higher than the range you've mentioned.
2. They are all part-time options where you generally work for a max of 20 hrs along with your studies. The nature of work could vary depending on the department and/or professor you are working with. It could be technical, administrative, coordination, managerial or a combination of all.
Such opportunities aren't limited to the second year students. Schools could offer it in the first year too.
Be aware that everyone is not as lucky to get free money from the good schools. You need to make them want
you to be part of their program. Only then will they offer you incentives to smoothen out the financial ride. The strength of your profile and the quality of your apps are important criteria that would be considered.
Here's the story of an old-timer on bschool forums (he's used to be quite active on GMAT Club too as bblast for his test prep phase) who got a 100% MBA scholarship along with a stipend
from the first year. You'll find other stories of applicants who've got partial scholarships and TA/RA/GA type of opportunities.
Sameer Kamat | Founder - MBA Crystal Ball | Email: info at mbacrystalball dot com