I've never run into a coil that just 'weakens'. I have run into coils that just stop working (broken winding...I had one just happen again last night) or blows a fuse (shorted winding). If it seems like the coil is sluggish or doesn't have enough ooomph, it's always been a mechanical issue with the linkages or coil sleeve, tarnished connector or dirty switch contact to the coil.

Yes there have been situations where the coil has overheated, at some point in it's life from being shorted on, and the inside diameter has decreased. This is still a result of something happening to the coil indirectly that caused the coil to become damaged.

These may or may not include all coils, but probably a majority of the more common ones.

https://www.flippers.com/coil-resistance.html
http://www.pinballmedic.net/coil_chart.html

Transistors are typically always on the driver board or power board in the backbox or in the case of flippers on the flipper driver board. There will usually be about 20 to 30 of them lined up along the bottom.