In applying the rule of 20, it shouldn't just be rotely applied. Some consideration of the number of QTs held should also be considered. Generally you want to have at least 2 QTs as well as the points and distribution that get you to 20.
Occasionally, you might open slightly shy of 2 QTs if the distribution and suit quality are good enough -- something like ♠ x ♥ x ♦ KQJxxx ♣ KJ10xx.
If you hold ♠ x ♥ QJxx ♦ KJx ♣ A10xxx, you get the 20 point and distribution count but only have 1 1/2 QTs, so this would be a pass.
If you held ♠ xx ♥ KQJx ♦ xx ♣ AJxxx, you again get the 20 point and distribution count, but have 2 QTs so this would be a 1 ♣ opener.
5 cards in a minor are sufficient for a simple rebid of 2 of a minor. Responder needs to be aware that opener may have a 4 card major if the response precludes bidding ther major at the 1 level.