Upvote:2
1) While I am on a business visa, is my family allowed to stay with me?
Yes, if their visas are granted.
2) Will I able to rent a house in UK during my stay?
There is surely some sort of accommodation available for short term family visitors, but I do not know about the price and availability. You will need to find out about this before you apply for your family's visas, however, because the visas will only be granted if you can show that you can afford the cost of their trip. You can't expect to show that if you don't know how much the trip will cost.
3) While they are applying for their visas, what should they mention in the visa application, as still now their accommodation is not confirmed? Once I reach the UK, I will arrange it for them. I am traveling in September, and they plan to come UK in October.
You should arrange their accommodation before you submit their visa applications. The applications will otherwise run a much higher risk of being refused.
4) I want to complete their visa before I leave for the UK.
Then, as mentioned above, you should arrange accommodation for their visit before you leave for the UK.