If the luncheon is a special event such as a luncheon before a wedding then yes, bring a gift. If it is just an informal luncheon with either friends (no special reason) or business you do not need to bring a gift.
No. The same applies if you had a gift sent directly to them through a store. But if you feel you should bring something, a wedding card is always nice. And if you want to be sure they know about the donation (or to expect the gift), you can include a message about it in the card. Or you could take a bottle of Champagne etc., which is always a good gift for celebrating events.
I know you're doing a lot, but you do need to give a wedding gift.
When someone puts that on a wedding invitation, it's effectively saying, "you don't need to bring a gift". On the other hand, if they are a young, struggling couple, bring a gift of something that will help them get established. If you choose to, present it discreetly to avoid embarrassment to other guests who did not do so and to avoid seeming to show off.
No. It's not traditional to send thank you notes to those who attended your wedding, whether they brought a gift or not. But for those who did get you a wedding gift, whether it was given before, at, or after the wedding, you need to send them a thank you card within two weeks of receiving the gift. If it's been longer than two weeks and you still haven't sent a thank you card, do so now. It's always better to send one late instead of not at all.
Yes, but include a gift receipt in case they need to return it.
You can a bring a gift that is not gender specific. So baby items in neutral colors is an option or you could bring a gift card that the parents can use to buy what they need for their baby.
She may be in urgent need of money. You should forgive her and discuss with her wisely and quietly to know the reasons behind selling the wedding gift.
I don't think you should if you weren't invited to the wedding. In polite society, gifts are NOT to be expected. If you want to send a gift it is up to you whether you get an invitation or not.
Probably for the wedding unless you spoil her! =P
If you received an invitation to the wedding then you do not need to bring the invitation to prove you were invited. If you never received an invitation to the wedding then it is not etiquette to attend the wedding and you would be considered crashing the wedding.
Yes, if you give a wedding shower gift you will also have to give a wedding gift. Many brides register at different stores so you could ask her maid of honor; bridesmaids or her mother what stores she has registered at and then go to one of the stores and get a print out of the articles this bride has chosen and choose which one that best fits your budget.