How do I say "choose one of these"?
To answer your first question about  "do I have to choose among these, or can I choose any others?"

The following sentence is perfectly fine: 非得选这些里面的一个吗？还是能选别的？
It means must i choose among these? Or can i choose others? Which fits what you asked in english.

只有这些吗，没有别的？Using this is fine, but might come out a bit rude because it makes the listener think your expecting more and can come out offensive to some. What you had originally is fine.

To answer your 2nd question about lying:
其中一个在说谎，但我不清楚是哪一个
Which translates to: One of them is lying, but I am not sure which one.