XL 90 Trane fan not starting

I'm going to suspect poorly insulated ducts running in unconditioned space as a first guess. I don't know the layout of your system, but it's very common to take duct runs up into the attic, and even if they are wrapped with duct wrap (R3-5 typically) that's abysmal. If the ducts are poorly wrapped or not wrapped in spots, it gets worse. R-50+ is far more appropriate for hot air in a cold attic.

As for the furnace exhaust, it should be fairly warm - otherise you get to visit the series of questions that are on here about furnace exhaust (high-efficiency condensing) freezing up in low temperatures and shutting the furnace down.

Fundamentally, if your furnace is running 24/7 and the temperature continues to drop, it's undersized for the load - but one of the best ways to deal with that is to reduce its load by improving insulation and air-sealing (caulking things - the most boring, most bang-for-the-buck way to improve efficiency in most houses that have not already had that done). You could also add a second furnace to take some of the load, but then you'll be burning even more gas. You do not want a furnace that is much larger than your "design load" (ideally, your furnace runs 24/7 and maintains temperature on your coldest days) since an oversized furnace is inefficient .vs. one that's just the right size.

1. No. You may risk damaging your unit by running it in cooling mode when it is too cold out (although some systems have safeties around this), but heating in low temperatures should not damage the system.
2. No. A correctly functioning heat pump should not ever drop below 100% efficiency.
3. This is dependent upon the specific heat pump model. Often, manufacturers provide charts/graphs describing the efficiency at different temperatures, but I do not see one available for yours. Two data points are specified; at 47f it is rated at a COP of 3.5 (or 350% electrical efficiency), and 17F a COP of 2.42.
4. No, but the heating capacity is often close, in mild weather. Yours is rated at 33,400 BTU/h at 47f and 21,400 BTU/h at 17f. Measuring this requires two temperature sensors (before and after the coil) and an accurate airflow measurement.
5. Your system defrosts on a timer, after 30/60/90 minutes of compressor run time, depending on a jumper setting. (this is less efficient than smarter systems that detect increased air pressure from from frost blocking air movement through the coils).
6. Protecting the unit from falling ice from eaves, and from accumulation of snow, is a good idea. However, make sure to leave ample space so that the airflow isn't restricted.
7. It says on the side that your blower draws up to 2.3 amps.