I've worked with agar a lot, and made a few things from the HRC. Of all of the things you've identified as possible problems, I think the biggest likely ones are the quantity of agar, and the agar powder itself. Everything else about the cooling issue is normal. Agar powders do vary. You want to find one that is pure, unadulterated agar, not one that is setup to be a pre-prepared dessert as those are weaker.
If just for a laugh you want to try to save this batch, heat it back up until the agar fully melts, shear in a second amount equal to what you did last night, making sure it fully dissolves, then let it set again. I'm pretty sure that will work.
You can also pick up a sub-gram scale on Amazon for around $20. Thanks, drug dealers! They are very helpful when making small batches of "molecular" recipes.
What you're observing is called syneresis. Most gelling agents such as gelatin and agar will tend to lose water over time, especially as the temperature goes up (i.e. from refrigerator to room temperature).
What is in fact happening is that the squares are drying out and pushing water out to the surface, which is why the powdered sugar gets soggy or even absorbed (the starch in that powdered sugar keeps it stuck to the jellies).
Gelatin being thermoreversible, you can simply melt it and set it again; it'll be a little on the sweet side due to the increased sugar but otherwise fine. Of course, you'll just end up with the same results. You need to add a stabilizer.
Xanthan gum is very good at controlling syneresis and is pretty easy to obtain in health food stores or even supermarkets nowadays. Add a pinch of that and you'll get much stabler results. Another additive I've used to stabilize agar-based Turkish Delight is locust bean gum (carob), although I'm not 100% sure if it works as well with gelatin.
Sometimes, you can just let them dry out - periodically wipe the excess water off the surface and hope that it stabilizes. But be careful; if it's not stable because you didn't use enough gelatin (or didn't use strong enough gelatin) then you might end up with a puddle of goo instead. So if you plan to try this, monitor it carefully.
Personally, I'd recommend tossing it all in a pot, melting it, throwing in a bit of xanthan gum, and setting it again. It'll be fine.
Best Answer
Grainy means your sugar formed crystals during the heating process. Lemon and other acids retard the formation of crystals, which is why one came out better than the other.
I'd suggest adding some cream of tartar to the other one (which should do the same as the lemon, but without changing the flavor).
In general, to lower crystallization, you should make sure the pots are absolutely clean, and then take great care not to stir or jostle the mix during the heating process. You can also add a little corn syrup, if you roll that way (adding acid actually inverts some of the sucrose into glucose and fructose, which is why it helps to add acid, but you can also just add glucose, in the form of corn syrup. I wouldn't use honey, because of it's water content.)
Hope that helps.