Ask Nava. I wouldn’t worry about matching genders. Go with whatever sounds nicest.
No! Unless you want it to be Heaven’s Port.
puerta = door
puerto = port
However, both “puerta” and “cielo” are nouns so to be correct, it should be Puerta de Cielo.
I’ve been lurking here for some time and I joined to post in this thread 
The correct translation should be “Puerta del Cielo”. Puerta de cielo is not wrong, but it’s not the most correct way to say it.
Also, from the first post. “Casa poco” is something like “House few”. I assume you wanted to name it “Casa chica” (small house). Casa grande and casa chica has some weird connotations in Spanish, or at least in Mexico. Casa grande = your wife and family; casa chica = your mistress. I doubt you’d want to use those, heh.
Good luck! 
Why not just go for the amusing “Fircombe Hall”, like my sister did?
OK, this is an interesting distinction. I think in this context you are right. However, I would perceive a slight difference in meaning between the two, and it would be thus:
“Puerta del Cielo” - Heaven’s Gate/Door. Heaven is a proper noun here (del is a contraction of “de” (of) and “el” (the), but of course it isn’t translated literally as “Door of the Heaven”, as the article “el” is a more common identifier in Spanish than in English)
“Puerta de cielo” - Heavenly/cestial door. Since we are attempting to use cielo, a noun by default, as an adjective, we use de. This differs from English, where two nouns can be placed together and one automatically becomes an adjective (e.g. “Brick House”). This was the context I was thinking of, but since you are using it as a proper name I would agree with Nell that “Puerta del Cielo” would probably be most correct.
Clear now?
Star Chamber.
On the shed, “Please do not taunt the bear.”
Next to the fire pit, “No witch-burning on Thursdays.” Or perhaps, “Witch-burning on Thursdays only.”
Casa de Pepe!
“Are you Pepe?”
“No, today I’m pretty much draggin’ ass.”
No clever suggestion.
Just wondering what the wooden tripod-ish thing is in your backyard?
Actually, given my liking of the Anne of Green Gables books, I immediately thought of calling your house “Patty’s Place.” Which is even more fun if your name isn’t Patty. 
As for the shed, I’d suggest, “AREA 51, Annex.”
Dude, it’s either “The Sin Bin” or “Chez Whitey”
Puerta Estelar and Las Puertas del Cielo
I am honored. Welcome!
Ahhhh, if only you knew me better.
In person it looks better. It is a split rail fence corner post with the rails going to the ground. The piece of plywood on top is where the blue jays get their peanuts. The post is used to support a clematis. ¿Entender, mi amigo?
That is the only tripody looking thing I can see…
Of course! How silly of me not to recognize it. Other than the fact that I’m generally familiar with fence posts that are part of a fence instead of standing by their lonesome in the center of a lawn, and split rails that run horizontally between posts instead of into the ground at an angle. Wasn’t sure what was mounted on that top platform - shoulda figured peanuts!
How many jays do you figure that stucture could support at one time? Couple thousand? No harm in overbuilding!
Maybe you could name your home - or at least the rear acerage, “The lone fencepost rest.” Or “Fat bluejays welcome.”
For the new VunderLair, I’m having a sign made announcing your arrival at
“Belle-Lea Acres”.
The best one I’ve ever personally seen, and one I can’t use because it’s not my last name, is “Coffeygrounds”.