Sending out thank you letters

I'm not sure what you mean by "people," but it is absolutely customary for the bride & groom to send thank-you notes to all the guests afterward. Thank them for their gift and for being there on your special day. It is considered rude not to do this, at least in the US. But it doesn't have to be a whole letter, just a small card. You can buy them in bulk, similar to how you would buy invitation cards.

You should always send thank you cards after weddings. I know the younger generations are not used to sending them (like us slighter older brides), but it’s very rude not to and will be something people remember if you don’t.

You should send a thank you card for any gifts that you received. You don't need to thank people for showing up to the wedding.

You should definitely send a thank you to anyone who gives a gift.

it would be up to you whether you send to anyone else.

You send thank you notes to anyone who sent you a gift. If they send the gift before the wedding, you send the thank you note before the wedding, too. Otherwise, you send it as soon as possible after the wedding.

Yes ! It is a polite thing to do

I feel just sending cards to those who gave gifts is fine. It can be seen as passive aggressive if you send a card/letter to someone who didn't