USB synchronization security issues I've got an Android phone. I have just reset it to its factory default settings and set a password for unlocking the phone. However, even when it is locked and the screen displays a text box with a text entry keyboard, hooking the phone via USB to Ubuntu Linux 12.04 LTS out of the box causes a popup to show up above the password request screen, which allows you to confirm the mounting of the phone's SD Card onto the filesystem in location /mount/328D-1EEE . Of course, the SD card could be removed from the phone and read using a card reader anyways, so perhaps this isn't as much of a security concern.

On the other hand, is it possible to read and transfer files to and from the phone's "internal, rather than external, memory", and to and from that little bit of space that is present on the phone's SIM (Subscriber Identity Module) card? If yes, then is this possible by mounting the internal memory or SIM card onto the Linux /media directory? I don't see these ones automount when I connect the USB cable, so I'm wondering if there is a way to do it manually.
What memory is offered on USB-Plug differs between devices. Most of them offer the external SD-Card (if present), some the internal eMMC card. Some even seem to offer a virtual CDRom drive (probably containing some device-specific stuff like drivers). But I've never heard of any giving access to the SIM this way, or even to system ressources. Of course, at least the latter is possible using 3rd party utilities (see Zuul's answer for an example). But access to the SIM should be almost impossible this way.

This all applies to Android up to Gingerbread. Starting with ICS (4.x), things become a bit different as UMS (USB mass storage) support was swapped in favour of MTP (Media transfer protocol). But basically, above said should still be true as to what is possible to access and what is not.