The Tropical Fruit Forum

https://www.youtube.com/watch?v=o2NtBCS2_WQ

Just got it into the ground.

location is about 12 miles from the coast, so I would consider it solid zone 10 (between 10a and 10b)

That's a lychee and tree fern you see up in the top left in the picture.

This is a bigger specimen than most people have tried, so it already has a well developed root system and may have a better chance of surviving. This guy wasn't cheap. But it's a big beautiful plant. (yes, purple mangosteen)

Lychee are a very finnicky fruit, but the payoff when you do get a good harvest is well worth it. It can be a little hard getting lychee to reliably fruit in their optimal habitat (in Southern China). All the more so when they are in a less than optimal climate. Southern Florida probably has the climate closest resembling Southern China, more so than California (dry) or Hawaii (almost no Winter cold whatsoever).

Designing a system to drain out condensation in the pipes shouldn't be too complicated.

I don't see any reason why above ground (or shallow in ground) heat banks couldn't be used, assuming they were well insulated.
It could just be as simple as multiple stacked plastic brick containers of water, encassed in a double layer of pumice-rich concrete (low thermal conductivity). It would probably need to be  somewhere around a fourth of the ground surface space of the greenhouse though, in size.

It's not just the earth's heat. Heat that builds up in the greenhouse during the daytime is pumped down, using the earth below as a heat bank. The temperatures down there aren't very warm, but it's enough to keep the plants from freezing during the night. Instead of venting the heat out in the day, a fan circulates air down into pipes. A depth as shallow as 12 feet is enough to be functional.

Here's a citrus labled "citrumelo" at Jungle Fever Exotics.



It has a few blossoms on it.

They also have a small Yuzu in a container.
He doesn't have a greenhouse, he keeps all the plants outside.

Satsuma is blooming

A lot of this is totally climate dependent. In the hot dry summers of Southern California, plants tend to do better in a little bit of shade. Even plants that are said to do best in full sun. Somewhere further North with cooler temperatures, more sun is better.

In Iceland I definitely would not worry about citrus getting "too much" light.

For more of an academic interest, you might be interested in some of the more obscure Japanese varieties. These types may not be as easy to find. Keraji, Kinkoji (known as Bloomsweet grapefruit in the U.S.), Kunenbo (likely you will have to go to a Japanese botanical collection for that, quite a history behind it).
Some other uncommon interesting ones to grow would be Duncan citrumelo, pomelo (C. maxima, the ancestor of grapefruit), citron (the ancestor of lemons, and there's a Giant Etrog citron variety that may be interesting), and Ichang Papeda.

I don't know if there's any possibility of using the greenhouse space as a dual use citrus breeding space. I realize Iceland is too cold to grow citrus outside, but there are people growing certain species and hybrid citrus in England and Germany. Maybe you could use your space to try to breed cold-hardy varieties that taste better. That doesn't really require much work, just knowledge. Most of the work is just in growing and taking care of the plants, which you're going to do anyway. Maybe get a volunteer citrus breeding expert in there to collaborate on the project. This citrus guy could, in turn, get advice from many people in other countries on what different crosses to try to breed. Your greenhouse could turn out to be pretty valuable for posterity.

I'm doing cold-hardy citrus breeding work and wish I had some greenhouse space to leave my small seedlings until they grew into bigger fruiting plants. Then I'd do the pollination of the flowers by hand and collect the seeds from the fruits, to grow new hybrid seedlings. Growing little seedlings doesn't take up much space and I can do it in my home, but growing all those big fruiting plants would take a lot of greenhouse space. Someone to keep them watered (which you're going to be doing anyway in your project). Unfortunately I don't live in Reykjavik.

For mandarins I would recommend Satsuma and Shasta Gold. A lot of people love Page too, which is pretty similar to Minneola tangelo (also very delicious and a good one for your collection).
Kishu mandarins are also very easy to peel and very small (seedless too if they don't get pollinated), very fun.

Another thing I'd suggest to really save on energy during the night is using geothermal heat banking. This basically fans air through pipes running into the ground, so heat during the day gets stored in the ground. There are several videos on this, you might look into it.

https://www.youtube.com/watch?v=o2NtBCS2_WQ

https://www.youtube.com/watch?v=IZghkt5m1uY

A good depth would be 3.5 to 10 meters.

No, the latest investigation pinpointed pesticides as the cause of the death, since those children peeled off the skin by biting into the exterior. They were using some dangerous pesticides on the lychee trees.

here's a keraji seedling

Fruit trees grown from seed usually take longer to begin producing fruit than those that are grafted.
This is because inducing a slight degree of incompatibility diverts energy from tree growth towards fruit production early on. (Probably because the nutrient to energy ratio for producing fruit is different than growing branches)

Of course Duncan is the gold standard for grapefruit flavor.