You won't get shocked by the wires, but unless you pull the fuse, you may keep starting & stopping the furnace as you make the connections. Best practice would be to pull the fuse.
That is correct. If you have the combined AC & furnace thermostat is is a bit more complicated, and the thermostat may be on a different fuse than the furnace. If you are replacing the furnace only thermostat, the furnace supplies the power for the thermostat.