Hello 2 wheels!
The Czech Republic is fine country for cycling. My wife and I were there two weeks in May 2004. We made an unsupported bike tour. The map with the track of our route is available on my home page http://www.velo-idea.narod.ru/Chehia.htm . I would recommend you to visit the province Moravia that is eastern and south eastern area of the country. It is very beautiful land. I liked especially small provincial towns and picturesque villages. Slovakia is much more hilly country. There is much colder in the mountains in October. I wasn’t there, but I was in Carpathians in Ukraine, climate is the same.
Highest daily temperature in Moravia is +15C in the middle of October and +10C in the end. Night temperature falls from +5C till +3C correspondingly. Precipitation level is pretty low - 40 mm.
There is no problem to choose a route in Czech, the network of nice back roads is dense, grocery and provision shops, café are everywhere. We bought in a bookstore the particular 1:100000 map “Cycloatlas” that describes 20000km of marked bike routes over the country. Hotels, hostels etc. are marked on that map also. I think accommodation is not a problem in October at all, so you need not book apartments. If you like stealth camping, it is possible too, except national parks of course, but I don’t know if it is legal in Czech.
As to language barrier, I can say that the second language is German there, so you have to use a phrase book. We were in simpler situation, because Russian, Czech and Ukrainian are a bit similar Slav languages, and nevertheless we used the phrase book.
I wish you good luck.

Alexey