50 Amp Flush Mount Shallow Single Outlet, Black

#4 AWG Copper.

Yes. Be sure your wire is sized for the breaker amperage. The Tesla will also need to be configured via the charging screen, for the breaker size. (I have a Model X)

If your cord has the same configuration and amperage rating as this 14/50 NEMA receptacle it should work just fine. Take a picture of the stoves plug and match it to the appropriate receptacle at HD. Plugs and receptacles have different ratings. Check your owners manual for power rating of the stove to be sure you match it with the rating of the receptacle.

If your cord has the male configuration of the female receptacle and has the same or more amperage rating as your cable feeding the receptacle it obviously will work. The question is what amperage is your dryer demanding. As long as it does not exceed the breakers rating you're fine. You also should know if the cable from the main panel breaker to the receptacle has a gauge large enough to carry the dryers demand.

1 gang box. You will need a mud plate.

Yes

Yes, you can use a 240 V 4-prong plug with this receptacle and it is rated up to 50 Amps.

This has a "50" amp rating, so it is not advisable to draw more amperage than the receptacle is rated for. If you don't need 60 amps just downsize the breaker in the panel to 50 amps. If the cable from the panel to your garage receptacle is a gauge that can carry 60 amps you can certainly feel assured it will carry the 50 amps.

yes

It depends on your RV. This is the receptacle for most 250 Volt, 50 Amp RV outlets.