The question you should be asking yourself is whether 35 K Qatari Rials (not Dinar)is justifying what you are joining as...the Grade and Area of Work etc...

And Saving Potential is very very individual based.

You can easily save 15 K a month...or to put in another way, you can comfortably live off 20 K a month.

Q1. If you intend driving, any place in Doha- Sadd, Najma, West Bay, Marriot Area etc decent localities to stay
Q2. In the areas mentioned above, the rents will range from 7k- 15k for good 2 BHK accommodation.In Abu Hamour, you can a decent separate villa for 12-16 K.
Q3. Sorry, not dealt with Real Estate Agents in 3 years now...so would not know. But try to always speak to the OWNERS and not Middle Men.

Congrats and good luck