Photos (the new one) opens automatically when I dock my iPhone. Is there a way to turn that off?

With your phone plugged into the computer open the Image Capture app. Your phone should appear under devices on the upper left of the page. A small icon should be in the lower left corner of the page. If not then click on your phone under devices and check again for the icon. Clicking on that icon should give you the options for what action to take when the phone is plugged in.

Yes. With the iPhone connected look at the left side of the bar near the top of Photos (below the red/yellow/green buttons at top left). Remove the check mark in the box before "Open Photos for this device."