Having beamed a communicator into a prison for Archer previously, no one even suggests beaming out the communicator this time. However it was explained that the exact location of the communicator was unknown and unable to be located on sensors which explains why it couldn't be beamed back.
When Archer and Reed are back on the planet again, they are being captured and their technological equipment confiscated. Somehow they still all seem to be able to speak in English with their captors. However, the universal translator devices are very small and could have been missed by their captors.
When the aliens use the words "surgically altered", they are referring to the fact that Archer and Reed had the crests on their heads removed by surgery and then had makeup-style appliances to replicate them. From the point of view of the aliens, this is the correct usage, as they believed they were all part of the same species. After that, Archer and Reed used similar terms to attempt to deceive the aliens.
Archer had used the same term when he realized they needed to be made up again to return to the planet, but this could just be hyperbole, in that they had literally just stripped off the makeup a few minutes before.
Archer had used the same term when he realized they needed to be made up again to return to the planet, but this could just be hyperbole, in that they had literally just stripped off the makeup a few minutes before.
In several scenes from inside Archer and Reeds cell you can see that the cell bars have wood grain indicating that they are made of wood and not metal. Unless the wood on that planet is extremely strong a good kick would have broken them.
When Reed and Archer are back on the planet's surface, Reed has a locating device that determines where his missing communicator is, within a few feet. Yet earlier on the Enterprise, he inexplicably fails to use the device and spends a great deal of time and effort manually searching for the missing communicator everywhere on board ship, as do Archer and Hoshi.
After Archer's failed attempt to martyr himself and Malcolm on his newly-discovered altar of non-interference, T'Pol rightly points out that such a sacrifice would've been in vain because great damage had already been done. Perhaps in his lust to get himself killed Archer overlooked such a blatantly obvious fact. But Starfleet would never tolerate such reckless, negligent stupidity in the commanding officer of a starship.