Need info about adigrat, ethiopia

1. how is adigrat? the place as well as university?

is in northern region tigray, an small but important city.

2. is adigrat a developed city like adis ababa or very remote village?

is not a village but not like addis ababa.

3. how to reach adigrat? how far is it from addis ababa? is there an airport in adigrat?

no airport, luxury bus services like selam and skybus are available there are other modes to it around 350 km from addis
4. how much money am i allowed to send to india? like libya doesnt allow sending more than 30% of income.

100 % including the bank charges.
5. how much should be my salary as they r not providing me accomodation but only air travel once a year.
i think they will give you travel once in 2 years
6. it was written on their site that salary would be in the range of 3000-4000 USD. will this salary be sufficient if i live alone in adigrat?
yes it will be.
7. how much is rent for a small furnished flat or a studio apartment in adigrat? i have seen on this  site that flat rent in addis ababa is 1200-2000 USD. if this is the case in adigrat then i think salary will not be sufficient for me.
you will not get furnished flat or studio apartment there, university will give you very basic furniture and the house you will get around 100 usd to 200 usd monthly.

first reply is fine.
BUT you will find it virtually impossible to get money out of the country.
You will also get constant power cuts and water cuts.
Also the phone network is the worst in Africa as is the internet.

adigrat is in tigray region closer to  mekele. you can fly to mekele and take mini bus to adigrat or bus. from addis it is around 850km. rent a flat in adigrat or a villa cost u $100 per month which is very nice house.
the salary u mentioned $3000-4000, u live like rich ppls and u cant finish even u torn it every day  some hundrends birr per day in adigrat