Piece Development for Beginners

Is it a general rule that your development is complete when you have castled, connected your rooks, or connected rooks without castling?

It's complete when all your pieces are developed so that would generally be when your rooks are connected, It would be unusual to connect rooks without castling. 

Yes. it is unusual; but, the Cochran and Fried Liver gambits are aggressive gambits which allow for black to capture with its king and eliminating blacks castling rites. At least now I understand that development can occur with or without castling.

Castling isn't mandatory, and neither is having connected rooks.

Connected rooks is powerful, but rooks usually see their best use in the 2nd half of a game, especially if the rooks are connected.

There are plenty of opportunities for an unconnected rook to be very useful in the first half of a game.

Occasionally I don't get a chance to castle, but less often, I make the choice *not to castle.  

*usually I wasn't given a chance to castle early, and I'll get a chance to castle, but decide I'd be better off keeping the king in the center and playing the flanks. Sometimes I win, sometimes I lose. lol

Hi, thanks for these explanations it helps me a lot.

Usually, even if rooks are connected early in the game, it's more common to act as if the rooks are unconnected, since the lack of open files and ranks severely restricts rook movement. But a rook can still be a very powerful piece, even when it's not moving.

Remember, general principles are guidelines only. It is more important to play the position on the board than to blindly follow a "principle".

Having said this, this link may help:

https://www.chess.com/article/view/the-principles-of-the-opening

Good luck. And by the way, if you have not already done so, buy a few chess books aimed at beginners. I highly recommend Play Winning Chess and Winning Chess Opening by GM Yasser Seirawan.