Elena
"Are there any issues with PIX 501 to receive and send a packet on the same outside interface?"
Unfortunately it won't work with a Pix 501. The feature you need is called "hairpinning" but this is only supported on pix v7.x code and later (also supported on ASA devices). The pix 501 cannot run v7.x code.
Pix 515E, 525 and 535 are the only pix firewalls that can be upgraded to v7.x code.
Alternatively a router can support hairpinning.
Jon