In cold climates, is it a good idea to shut the main water valve and drain all internal water pipes before leaving on an extended trip?

Yes it is, and leave all the taps open in case any water in the pipework that cannot be drained out can run out of the Tap as frozen water expands as it thaws and nmust be able to expand with out busting a pipe. Just close the Taps when you come back and turn the water back on.

The purpose of draining the water lines is to prevent freezing. An easier method is to keep the temperature in the building above freezing. If you leave for 2 or 3 MONTHS, it is worth draining the lines. For 2 or 3 weeks, you are better off just leaving the heat set at 40°F or above.

Good insurance against any problems.

Shut off the main, drain the lines, leave the taps open.

YES.

My next door neighbor went to Fl. for the season. We had a blizzard and the temps were below zero. Power went out for 18 hrs. He had one heck of a mess when he came back. I'm luck. I have a wood burner downstairs.

If the power goes out like his did, you'll be in his shoes.

That is a safe thing to do to prevent bursting pipes.

Consider insulating the garage pipes, this coming summer.

You can add prestone to toilet tanks and bowls rather than empty those.

Yes. If your heating system fails, there will be no water in the pipes to freeze. This will also help thieves when they come to take all your copper.

Sounds like that's exactly what you should do. No downside unless you turn the heat off. Water can freeze and break tubing if left in areas where it's trapped even though pressure is not there.

yes- turn off water main winter or summer--you never know what will happen--rubber hose to washer could burst, some one turn on outside faucet, etc. (I do this even if leaving a week)

You should also shut off and drain your water heater...

I would set the thermostat on 4C/37F as frost protection.