They can as they will support the wire into the box. The deciding factor should be the cost. A BX connector costs about four times the price of a romex connector. Also to keep in mind is that most junction boxes these days have their own built in clamps.
Copper or aluminium.
Assuming 220 volts service 5000/220 = 22.72 Amps. That equates to 10 AWG Romex.
THHN is a heat resistant thermoplastic insulated conductor, usually a single conductor. Romex is a brand name for a nonmetallic sheathed cable, it has multiple conductors inside, the insulated ones are insulated with THHN insulation.
Romex is a manufacturer's wire cable trade name, the 10 refers to the size of the wire inside the cable set. A #10 AWG copper conductor with an insulation factor of 90 degrees C is rated for 30 amps.
Yes
yes
Not legal
Yes unless there were some overarching electric code reason why conduit was used in lieu of Romex. if in doubt ask an electrician.
In romex, 14-2 means two conductors, 14AWG each, and 14-3 means three conductors, 14AWG each. Note: Normally, romex has a ground, so the designation is more likely to be 14-2/G or 14-3/G.
Standard Romex is a three-strand, solid core wire, individually insulated, in a common sheath to make it easier to pull. For a short time, some manufacturers were making romex with aluminum because the cost of copper was so high, but the aluminum wire was not as good as the copper, and the practice was discontinued.
The exact year that Romex Wire came out is not listed on their website. However, they do say that they have been selling the wire for over 88 years. I have found the year 1926