Also curious as to how much cost can be to rewire a 1400-sf house (3 bedrooms, single-story), and how much replastering is typically necessary.

Rewiring costs depends on many things (like accessibility and local labor rates) which will also determine how much disruption of the finished surface is required. The electrician can make an estimate if such rewiring is warranted.

Depending on the house, the 50's were right on the cusp of the modern wiring (grounded circuits, etc..) so you might be OK. You may be a little lean on service capacity for things like air conditioning and electric dryers however, but that wouldn't warrant an entire rewiring.

There are not many items that use a ground on general use circuits (lamps, clocks, vacuums, etc.) so running a third line just for the sake of having it does not really do much.

You can run 3-wire circuits for things that DO need a ground (computers, TV, stereo, other electronics) to the location needed.

Copper wire does not wear out, but the insulation can be damaged.

A leading cause is over-wattage bulbs in ceiling fixtures.

The old wire was 60C insulation with a lot of fixtures designed around 40 W bulbs.

Using 60 W bulbs (or even higher) overheats the wire insulation in the box behind the fixture (rarely a problem with chandelier/hanging fixtures though).

Some older ceramic bathroom fixtures were designed around 25 W bulbs, and the fixture wires are often thoroughly cooked, let alone the box wires.

The cost of rewiring often ends up including wall repairs and painting, so electrical is only part of the final bill.

This is typical in 99% of homes and not a sign of a problem.

Rarely has anything to do with wiring age or quality.
The POCO is not an infinite source of current.
When a large load (especially an induction motor) starts up it appears as nearly a short circuit and can pull 3-5 times its 'running' current.
The current quickly falls as the motor comes up to operating speed.
During this time the voltage from the POCO sags in your house, and the lights momentarily dim.

"Also I don't know the history of rodent activity in the garage area before we got here years ago, so want to make sure the insulation in that area looks OK."

If you can see the cables check for damage.

If the cables are hidden the only thing that can really be done is to open walls and look at them, or run a mega-ohm meter ('megger') to measure the insulation resistance.

A megga-ohm meter puts voltages at (or even above) the insulation rating and measures current leakage through the insulation.
House wiring has a rating of around 600 V AC, so voltages around 840 DC are the starting point for checking the insulation (the peak value of a 600 V sine wave).

Newer equipment is better since it can measure lower leakage currents without using even higher voltages.

It is slow work since sections of the wiring must be isolated before running the test.

It is more commonly used after lightning strikes to check for hidden damage.