Ok to answer your questions in order:
No. What it looks like here is a bad cable, or a bad connector. If the mobo can detect the external drive from BIOS, then it is a problem with the internal components there.
I have no idea either, but you could look it up easily. I stay away from laptops because of hardware issues. Though I should learn so I can fix my laptop when I go to college.......
No, I think the drive is dead. Do you have another computer? Put the drive in there, and see if it is detected. If not, then it is dead. Keep it if you want to get the Data off.
Now as for a solution!
I am assuming that the cable came with the computer, so go buy an aftermarket cable, and use that on the new internal HDD and see if it works.
If it fails to detect the new HDD with its new cable, then it most likely IS a mobo issue, which is a B**** to fix in a laptop. Buying a new one might be easier.