I am currently living in Mexico City, I decided to order an iPhone, which came already unlocked, it works perfectly with my local SIM (firmware 1.0.2), but I was wondering...could it harm my iPhone if I try to install 3rd party apps now that it's already unlocked and working fine
No, 3rd party apps don't hurt the iPhone in anyway. The only way to hurt the iPhone is a user error. Just install Installer.app and the Community Sources it comes with.