I heard, that some resources (or maybe all) are limited. The number of lengths seems to be limited to 2^8 (1 byte). Are there any other limited resources and if yes, which are these or where can this be looked up?
all registers have a fixed number, counts, lengths, (dimen and skips) boxes there are 2^8 in classic TeX but almost all formats use etex where this is raised to 2^15. xetex also allows 2^15 and luatex 2^16.
Other fixed allocations are math families (16 in classic tex and etex, 256 in luatex and xetex).
The TeXBook or TeX by topic have the details, along with the manuals for etex, xetex or luatex for the extended behaviour.
there are other fixed resourses (other than luatex which uses dynamic memory) total memory, total number of control sequences, etc but these days these limits rarely affect normal documents.