On the garage door opener, opinions vary as to how important it is to follow the underwriters laboratory safety guidelines for unattended operation of garage doors.
If you just hotwire a relay like the one you mentioned, which is UL approved for appliance control, but not for garage doors, then you forego some safety features like the beep before it starts to close.
If you’re willing to spend about $50 more, you can get one of the
UL approved solutions like the Telgard or the Linear GD00Z.
(If your housemate pays you rent, Local housing codes may require you to use a UL approved solution, btw. Individual homeowners can make their own choice. The hotwire option is used by a lot of people, although I’d go the UL route myself. It’s a personal decision.)
The linear is also very popular, and GaryD has written a device type for it which works well with ST.