Generally, the larger companies tend to perform in venues that seat upwards of 1000 people, but from time to time perform in small, very intimate theatres. It really depends on the facilities available, cost and the size of the typical audience.
As to casts, they range from a single dancer to upwards of 100, if you count extras. Outside of full-length ballets, the largest cast is probably in Balanchine's "Union Jack" which has more than 60 dancers, I think.
Funding really depends on the company and how much they can make from tickets sales. In Europe, many companies receive the majority of funding from the government, and only rely on corporate and private donors for a small perecent of their budgets. In the US, companies spend a great deal of time raising money - some comes from governmental organizations, but usually most is raised from private donors, galas and private trusts/non-profit organizations etc. And it's often not an easy task to keep a company in the black - debts are not uncommon.