By the looks of some of the sizes it seems to me they made drums up until the early mid 80's?
Amati was originally commonwealth of craftsmen who made wind instruments (many of them were Germans, as Kraslice really had strong german minority). I do not know whether they made drums and cymbals before WWII (I've seen something, but I can't be sure), but sure thing is that they were making them in 60s (I've seen some old drums that could be from 50s but can't say for sure whether they were Amati). From that time, three (four) main series were released.
(0.: Seen just few snares, old barrel-like lugs)
1st: http://gilnar.rajce.idnes.cz/Amati/#39_1.jpg (60s)
2nd: http://medak7.rajce.idnes.cz/Documents_2/#Amati_281.jpg (new lugs)
3rd: http://medak7.rajce.idnes.cz/Documents_2/#Amati_259.jpg (deep drums, virgin bass drums (!), giant heavy racks copied from Pearl)
These informations may not be correct, but when I asked Amati company for some info about drums they said the documentation no longer exists. They only make wind instruments nowdays. Production of drums was halted in early 90s (I think whole "Amati drums" thing was just part of communist doctrine of completely independent east bloc. I can easily imagine some comrade saying: "Trumpets are from brass, clarinets are from wood. Drums are from wood, cymbals are from brass. Let them make drumsets!!!"). After that they were making "Magic" cymbals for a few years, but they were pretty bad.
Did they make their own shells?
Yes. As for material... at least 2nd and 3rd series is made from beech.
Not very good. Wood isn't of big quality, edges are often uneven or rough, tom mounts are lead into drums and toms were often manufactured in odd sizes (too deep or too shallow) and without resonation heads. Even so, if you manage to find drums that are in good condition, with lugs on both sides, maybe do some work on the edges and put some good heads on them, they might sound quite good. But they'll never be something really stunning.
Their main advantage is that they are cheap, easy to get, and while Stagg, Peace, Ashton or similar brands fall apart after half a year, Amati hold their own for decades (Now I'm not talking about their cymbals. They crack. Hardware is quite OK, but has some unpleasant weaknesses.)
Sorry for such a long answer, I hope you get some useful information from it :-)