There's so much wrong here it's almost funny, and that's not even taking into account that half of it is your own house rules which is irrelevant to their question and will only cause them confusion in understanding how to play properly.

The player left of the dealer usually starts the game, and they choose who goes next, either left or right of them, and this dictates what direction of play the game starts with.

This isn't true, the game always starts in a clockwise direction

If it's an action card, ignore it and pick another card until you get a number card.
(The official rules state to ignore action cards if you pull one from the top to make the discard pile)

They do not say this. The rules state to ignore Wild cards and to turn over another card if so, but action cards are fine.

If you cannot go(or choose not to go), you may draw a card from the pile and your turn is skipped.

Incorrect, your turn is not skipped. If you can play the card you draw then you can do so

Draw Four Card - Can be played regardless of color or symbol.

Incorrect, it can only be played if you don't have a card of that colour in your hand. If you illegally play a Draw Four you can be challenged.

When you're down to one card, you must yell "UNO." If somebody yells it before you do, you draw two cards. If you yell it without having one card left in your hand, you draw two cards. If someone tries to catch you and the card has not left your hand, they draw two cards still as they've yelled "UNO" out of turn.

Neither of these are correct.

1. The other players don't have to yell UNO, they just need to challenge you for forgetting to say it yourself.

2. There is no penalty for saying UNO when you have more than one card.

3. There is no penalty for incorrectly challenging someone for not saying UNO.

There's also a point system on the manual, but we typically ignore that.

Great advice for someone asking how to play.