Hi. I wouldn't worry too much about the poops. They actually eat them sometimes, which is normal. They have two stomachs and can redigest vitamins etc from their poops! So their poops are sometimes emergency food supplies! I think it makes them feel secure to have a few poops hoarded just in case there is ever a shortage of food!
They are not dirty or smelly - like little hard things really. If they start taking over a bit in the cage then spot clean the substrate.
Yes they get very upset and stressed about the nest being removed. I leave it alone unless it is pee'd in. If there is the odd poop in the nest I wouldn't worry too much - if there are quite a lot you could pick some out. I tend to find, when they have the big house, that the poops are kept separate from the hoarded food (although the odd one mixed in with the hoard) and the poops are kept in a separate place!
I have never worried about poops really and all our syrians have lived to a grand age. When you eventually do a substrate change you can remove any excess then, but I would still try and leave the nest in tact. Keep putting out strips of torn up plain white toilet paper in a heap (safest nesting material) somewhere in the cage - near the house maybe. They take it to build or refurbish their nest. When leaving the nest I find they refurbish it themselves and sometimes chuck out an old bit of nest and take in new nesting material to refurbish the nest.
Re the litter tray - she may kick sand out of it but I wouldn't worry - it will just sink to the bottom of the cage - or can be left - doesn't do any harm. Main thing is that she pee's in it.
Our last syrian used to pouch some of the sand I am sure! Because I used to find it in his hoard - maybe some clever hammy thing to help preserve the hoard! Both our last ones used to put substrate on top of the potty as well, after peeing in it (so it doesn't smell?)
Our last syrian did used to kick most of the sand out of the potty but usually left enough in to soak up the pee, although occasionally it would just be pee in there! But he still used it so the pee was contained which is the important thing. It is only really their pee that is smelly. They are quite clean little things otherwise, they groom a lot.
Shoebox house sounds like a good idea. When she is fully grown, if she is still small, then the lief house might be ok. Most people knock out the solid but under one partition so the house is open underneath (or that bit may get pee soaked) and you would probably need to knock out the inner dividing partition as well or the "rooms" would be too small for a syrian.
Re the house legs - you don't need to buy them. Before they started making them, I just glued on my own legs - wood dowels. Not much diy involved. I used ponal glue which is hamster safe wood glue, doesn't smell and sticks rock hard. It's expensive at first to buy but am still using the same bottle 3 and a half years later. The only diy bit really is cutting the dowels to the right length. What I did was rest the back edge of the house on the lip of the cage base and just stick a leg on each side of the cage, nearer the front than the back, and two legs on the front. That way they can all be the same length and not fall foul of the curved base underneath.
These are the dowels I got
https://www.amazon.co.uk/gp/product/...?ie=UTF8&psc=1
And this is the glue
https://www.amazon.co.uk/Ponal-44272...1821555&sr=8-2
But now that they actually sell legs, it is way easier! Again I put two on the front and one at either side not too far back so they are all on the flat bit of the cage base and that holds the house up fine.
Shoebox house is absolutely fine though and much easier and cheaper! I would put a litter tray inside though or it may get pee soaked.
I actually don't bother with a sand bath for syrians because, as you say, they just kick all the sand out. Our last syrian didn't like sand really. So I just use it in the litter tray. They tend to pee in the very back corner and sometimes sit in the front for a wash.