Can ElGamal encryption and ElGamal signatures be used together sharing the same key-pairs?
It depends.

It depends on a lot of things. For example a generator of 2 is great for encryption, but makes for awful signatures. If you use a generator of 2, then no. Your signatures will get broken. Then the encryption will.

Elgamal signatures are pretty controversial. They're tetchy to get right (see above) and there are many things you can get wrong. Also, they're large, when compared to DSA. DSA is a modification of Elgamal signatures and designed so that the size of the signature is proportional to the size of the hash, not the size of the key. They're thus smaller.

They were added into OpenPGP for RFC 2440, and implemented in GnuPG but not in PGP, because of security/implementation concerns that PGP developers had. A serious bug was found in the GnuPG implementation and then were removed from GnuPG, and then from RFC 4880 as no one was implementing them.

Ask yourself why you're doing them rather than DSA, research the problems people had in the past, and make sure you've done it right.

Jon