1) First off, will it be too hot and humid to the average person during this time?
It will be around 40 degrees C during the day, and humidity is usually very high in September, at least 60%. It is not very pleasant if you plan to spend a lot of time outdoors.
2) Is it possible to do it in the smallest Toyota?
Definitely, yes. Roads are good.
3) I will make reference to LP's sample itineraries, yet are there any must see sights (historical and culturally rather than bar and clubs)?
Check out Mutrah district in Muscat for the souq, the harbour and the Sultan's palace. the town of Nizwa in Oman is also interesting. In Dubai, check out the areas around the Creek such as Bastikiya and the Gold souq & Spice souq. Also Dubai museum is worth a look. In Sharjah, there are some interesting mosques, museums and souqs.
4) Is it possible to spend most nights in the hostels along the way without prior booking cheaply?
I don't think you will find many hostels in this part of the world - there is one in Dubai but I doubt you will find them in smaller places when you're on the road.
