Colleges in Himachal Pradesh

In all honesty, it depends on the pace of work done at your institute. There is a slight chance majority of your degree won't be completed at your own campus, but highly unlikely that you'll complete 4 years not being at your campus.
Again, it depends more at the pace of work and how fast the government gives out clearances to your institute. I have seen some work finished in a jiffy (I study at a government institute as well) and some which has been going on for years and is yet to finish.

It is good for Diploma programs. It provides various opportunities for students to grow vertically and horizontally in their career paths and also offer 100% placement assistance with partner organizations.

You will not get this college because your rank is very low. You can get government colleges with this rank. Try JEE college predictor to get more information and insight about college & branch which you can get on the basis of your rank:-
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=4067795.

Yes, you can take admission.

Depends on what college you want admission into. You can get into a lot of NITs with that rank, mainly you will be able to get branches such as Mechanical, Electrical, Civil. Cut off for CSE and ECE is generally very low for NITs so chances you get those branches are low, but you can hope to get one of those branches in internal shuffling once you secure admission into a college.

As it is an NIT, getting admission would be quite difficult there as you don't have any quota except the home state one. I can not say for sure that you will be able to get admission into ECE. So, I would recommend that you apply for other branches or look into other colleges. You can also apply for IIIT Una which has the same faculty and campus as NIT Hamirpur and has the CSE, ECE and IT branches. With your rank, there is a chance that you can get admission into IT or ECE in IIIT Una.

As it is an NIT, getting admission would be quite difficult there as you don't have any quota except the home state one. I can not say for sure that you will be able to get admission into ECE. So, I would recommend that you apply for other branches or look into other colleges. You can also apply for IIIT Una which has the same faculty and campus as NIT Hamirpur and has the CSE, ECE and IT branches. With your rank, there is a chance that you can get admission into IT or ECE in IIIT Una.

You have a very low chance of getting admission into NITs due to your rank. I would recommend you check out other institutions like UPTU etc. Depending on your state and look towards securing an admission there.

You will not be able to get either CSE or Mechanical as both of these branches close fast. If you do have a home state quota, you might get admission into these branches in later rounds. I would recommend you look into IIIT Una as it has the same faculty and campus as NIT Hamirpur and is also a government institute. You can get admission into CSE or ECE engineering in IIIT Una with your rank.