Disconnecting the Power Supply
The main reason for disconnecting the negative terminal on a car battery first is that the whole of the car body is linked to that negative terminal.

Disconnecting it first removes all the possibility of a short between positive and negative without going direct to the battery negative terminal.

For disconnecting individual items within the car, disconnect the positive first as you would with any other device.

As for powering chips without a ground (or \$V_{SS}\$) connection, the power will probably try and find its way out somewhere and yes, could cause problems.

Personally I usually turn off the power supply rather than unplug it live.