Mabrook first of all and welcome to Al Jazeera

I work for AlJazeera Network

4000$ is almost 14500QR is not a bad salary, infact this is a good start.

IF they told you that you are getting a villa then you are lucky, what you can do is ask for the allowance amount you will be getting incase you dont live in villa provided by AJI, then you can always select any villa or flat between your allowances, (you might be able to save more from allowance amount) this is what most employees do.

Visa does take time, 1 to 1.5 months at least. Be relaxed.