Words like "sailing, shopping, swimming' are activities... and are known as grounds (nouns) so we say I am going shopping. I am going sailing. To sail is a verb, so we say I am going to sail. I am going to shop. I am going to swim.

For 1 "going to sailing" is wrong. You can say "going to sail" or "going sailing" or "going to go sailing". I would say that the first is more "active". It is a subtle difference but "going to sail" is better if you are operating the boat, and "going sailing" is better if you are on the boat "along for the ride". But both are used in both cases.

Either I'm going sailing (could be now) or I'm going to go sailing (a plan for the future.) Either is used for a choice of two things. You can have either. You can have either the blue one or the red one. Neither is the negative. I like neither. I like neither the blue one nor the red one. So either...or Neither... nor