As long as your stick isn’t longer than...40"? It can be used. I don’t know exactly, I’d have to read up on it but there is only a rule about it being too long. I do know that a shorter stick makes it easier to control the ball, but I don't know that they have a too-short rule.

You can lift it in field hockey, that's why they wear those funny masks on penalty corners.

My young kids play in a rec league; the older one also plays for a club. It's big in the mid-Atlantic region. It's also much more popular for men in other countries. Male field hockey players are almost unheard of in the States.

No idea if there is an actual reason behind it, I just know it’s against the rules to use a lefty stick. A reverse (rotating the stick so the toe is on the turf) is legal, and a basic skill. If you watch the players you’ll see they do it all the time. (NB my kids play, which is how I know the rules.)

All players use a right handed stick. To turn the stick around and use it as a lefty would is called a reverse and is a legal hit.

The rule of thumb in the US is that the stick should come up to just below your navel. Europeans tend to play with shorter sticks than their US counterpoints, and measure from (I think) the top of the shoulder to the hand.

The short stick allows for better ball control. (My kids play.)