What are the risks of doing a PhD in a new department?
The risks are as you describe, although I suspect that the third item is not as serious (unless your advisor has a formal administrative role). 

The pros are that you will have a lot more input into how the curriculum and the program is shaped. As a new department, people will try things, and not everything will work. There will be many opportunities to suggest improvements and how to do things differently. 

If the parent university is well known, it's in their interest to make sure the new program succeeds, so you should also get some benefit from the level of attention paid by them. By bringing a number of faculty over, they've expressed "buy-in" to the new institute.