1) and 2) A voltmeter should be connected across (i.e. in parallel with) the voltage source to be measured. Your meter is in series between the 7805 output and the micro pin.
2) In the second pic the 5V connection is fine, but your switch will need to be debounced (in software, or by using additional components).
3) Read the datasheet for the micro and follow its guidance about capacitors.
Edit: The input voltage to a 7805 needs to be > 7V for it to regulate properly. Your LED is dropping the voltage too much. Run the 9V directly to the 7805 input.