I have not had any issues finding the next assignment, it may not be exactly where I want to go - but traveling requires flexibility. I generally start looking about 2 weeks from the end of my current assignment. Facilities do not post needs further out than that (typically). As the above poster said, I also take a couple of weeks off in between if I can.
The agencies vary on what type of housing they provide. You can always take the stipend and find your own housing if you don't mind doing the research yourself. If you take the housing, they are supposed to find you safe housing - it does not always work out that way. Everyone's view on safe/desirable amenities is different.
As far as insurance, some of the agencies offer that - some give you an insurance stipend to offset the cost. The tax home thing is a big deal. I am not sure how it would affect your pay if you don't have one. I would ask an accountant, you have to pay taxes somewhere.
You can PM me if you want my opinion on the agencies I have used so far.