Yes, I have noticed how you have to "equip" your houses, after desperately searching for my Castaway Cove.

Does that mean we are able to share those in any way?

When I did attempt to put my Castaway Cove in the shared back, I could not get it to work, so, I am not entirely sure you can. (I wanted to restart because I believe I chose the wrong death for my parents, since I was really trying to get Milo Graytail as one of my companions.)

From what I have seen, there is no way to transfer a house between characters. You can transfer Housing Items between characters using the Shared Bank but it doesn't look like there is a way to transfer a house.

I'm not sure why you want to delete your character. If you want a different type of Pirate, there are a total of 6 different Pirates that we can have. The way to get a new Pirate is to go to the Character/Pirate Selection Screen and press "New". Of course, the 'new' Pirate wouldn't be able to use the house unfortunately, any of the Companions your present Pirate has, or any of the items that say No Trade. If you do delete your character, any items purchased with Crowns would also disappear unless first transferred to another Pirate in your account.

If the reason is you want to change how you spent your Training Points on your Companions, go to the Character Management Interface, select the character you want to change, and press reset (lower right corner). This will reset all of that Companion's Talents and Epic Talents and you can make different choices. If you are a member (ie able to go anywhere without having to pay Crowns, usually monthly or yearly), then all it should cost is some Gold (the amount depends on your Pirate's Level - otherwise I think it will cost some Crowns).

Now, if the reason you want to change how you spent your Practice Points for your Pirate, go talk with one of the trainers like you were going to learn something from them and press the Reset Button (lower right corner). This will cost you some Crowns but it is a way to change your decisions without having to delete your Pirate and lose your house and anything else you can't transfer to another Pirate in your account.

Hope this helps.

If this does not answer your question, talk to support using the Help menu option (the Orange Question Mark) above.