As fschnitt points out, a comprehensive answer to this would likely be a chapter in a systems administration manual, so I'll try just to sketch the basic concepts. Ask new questions if you need more detail on specific points.
In UNIX, all files in the system are organized into a single directory tree structure (as opposed to Windows, where you have a separate directory tree for each drive).
There is a "root" directory, which is denoted by /, which corresponds to the top directory on the main drive/partition (in the Windows world, this would be C:). Any other directory and file in the system can be reached from the root, by walking down sub-directories.
How can you make other drives/partitions visible to the system in such a unique tree structure? You mount them: mounting a drive/partition on a directory (e.g., /media/usb) means that the top directory on that drive/partition becomes visible as the directory being mounted. Example: if I insert a USB stick in Windows I get a new drive, e.g., F:; if in Linux I mount it on directory /media/usb, then the top directory on the USB stick (what I would see by opening the F: drive in Windows) will be visible in Linux as directory /media/usb. In this case, the /media/usb directory is called a "mount point".
Now, drives/partitions/etc. are traditionally called "(block) devices" in the UNIX world, so you always speak of mounting a device on a directory. By abuse of language, you can just say "mount this device" or "unmount that directory".
I think I've only covered your point 1., but this could get you started for more specific questions.
Check this for further reading.