Is there a program that automatically tiles all (new) windows?
I'm not sure whether there are ways to automatically tile all open windows, but both BetterTouchToool (blog.boastr.net, free) or BetterSnapTool (https://itunes.apple.com/de/app/bettersnaptool/id417375580?mt=12) let you organize windows.

I'm not familiar with BetterSnapTool, but with BetterTouchTool you can configure your own actions, so you might be able to get what you want by using a series of built-in actions.