Key and signature sizes of NTRU and NTRU Prime?
The inconsistency of Ntru public key size is due to the fact that those are from two different parameter sets (targeting different security levels). The latest version of recommended parameter sets can be found from
https://eprint.iacr.org/2015/708.pdf

Ntru prime does not have a signature scheme as far as I know. 

NtruSign signature scheme is broken and is not recommended for use. The same group of people come up with a new scheme named pqNTRUsign which is secure against the transcript attack that breaks ntrusign.
https://eprint.iacr.org/2014/457.pdf

The reference implementation of both Ntru and pqntrusign can be found from
https://github.com/NTRUOpenSourceProject/ntru-crypto