supermario

Cherimoyas are difficult to judge while on the tree. If picked at the right time, it should feel like a ripe mango. I believe they do not ripen well if picked too early, but I'm not sure.

In my opinion, dragon fruit isn't all that great. Even the sweetest varieties seem a bit too watery. I'd compare them to a watermelon, but with less sugar.

I've never heard anyone call it that before. Lychees are not nuts.. I think they are technicaly berries(any experts out there?) Good varieties are sweet, flesh seperates from seed easily, and most will produce a small aborted seed(called chicken tongue seed) instead of the one that looks like a 'nut'.
To eat a lychee, you just peel the skin and pop it in and work the flesh off the seed in your mouth.. Or you could remove the flesh from the seed with your hands like I do. I prep a bunch and then sit down and scarf 'em down.

Oh!..and PLEASE try them cold. Pop the package in the fridge for about an hour or so and your good to go. Soooo much better! Longans too!

As for planting lychee seeds.. here is some info from Purdue's web site:

Propagation

Lychees do not reproduce faithfully from seed, and the choicest have abortive, not viable, seed. Furthermore, lychee seeds remain viable only 4 to 5 days, and seedling trees will not bear until they are 5 to 12, or even 25, years old. For these reasons, seeds are planted mostly for selection and breeding purposes or for rootstock.

You can read the rest of the info here: Lychee

Unfortunately, lots of the world's best fruit are not propogated by seed.

I think it's called 'Cuban Red' or 'Jamaican Red'