1.办酒的时候一定要请我们（的1），我们要喝喜酒（的2）。“的” in the brackets are not necessary. The best way to say this sentence is to remove “的1” and keep “的2”: 办酒的时候一定要请我们，我们要喝喜酒（的2）！ 2. 办酒 means 办酒席 (to host a feast; yo invite guests to eat, which can be a birthday party, celebrating children's birth, etc.). In the context, it means hosting a wedding feast.

I think the 的 is just a 语气助词 (modal particle), which has no concrete meaning. You can put it at the end of a sentence to make it sound more casual (informal). This is mostly done when you express your plan/intention to friends/acquaintances, e.g. 喝喜酒，一起吃饭, etc. I agree with Shanmei that you don't need to use a 的 unless you finish your sentence.

1. YES!!!!! Sorry I don’t know how to explain the difference between two 的 . But this sentence makes sense too when I delete the second 的, and the meaning are still the same （在这个句子里，“的”只是一个语气词，可有可无） 2. Yes