Ex Kotaite, but not an engineer.
If your brother wants to go and if your parents are supporting, only then send him. Regarding coaching, Allen is good, Bansal has not produced the result in recent years that it used to give 5 years back. When I was there Resonance was OK but not in top 2 league. Scenario has changed, so you can check the results and compare (compare classroom course results). Regarding schooling, non-attendance school can be done in Kota too and in Patna, too. When you go for admission there will be many people offering for that type of schooling with full detail. Fees will be more or less the same at both places but much higher...
more... than what normal students pay. If your brother is ready to work really hard for 2 years then Kota is not a bad place. If serious about it then do send him otherwise not. And regarding lodging you will get many hostels and PGs around the coaching centres which will be at a distance of 2 min walking to 15 min cycling distance. For food, there are mess at every nook and corner of any locality.