Both above answers are correct.
Also, to add and answer your other questions:
1) the factory fan setting does not turn the fan "on" until I believe the temp has reached upwards of 221*. The stock dash "idiot" temp gauge is not accurate at all - as every 94/95 5.0 will show a different needle location on the stock gauge, some registering hotter, some cooler. The absolute best thing you can do is add an aftermarket temp gauge which will show actual numeric temp readings. There are even radiator caps now w/ temp sensor & numeric readings on top of cap OR you can get a hand held laser temp reader to read the engine temp by pointing at thermo housing, hoses, engine etc...
2) a cooler thermostat will not have any real bearing or benefits in a 94-95 5.0, unless the owner has the car manually tuned via the EEC (ie: shop, or user hooks up to EEC and manually adjusts the software parameters for fan turn on/off temp settings). Stock thermostat should be 195*, if it's still a stocker in your car. If N/A, don't go with a thermostat any cooler than 180*.
3) IF the fan is NOT turning on (once it reaches optimum turn on temp OR by you moving the HVAC control knob to A/C, Defrost or Mix), then there are (4) possible reasons for failure:
A) The CCRM module - black box which is mounted next to the factory coolant overflow bottle retains the relays for the fan & fuel pump. It's quite possible the fan relay has failed, which will prevent the fan from turning on. Fix is to either bypass the relay entirely by using an aftermarket fan controller OR putting together your own manual switch harness OR by simply replacing the CCRM module.
B) The fan motor has seized. If this has occured, you won't be able to manually spin the fan blade. Fix is to replace entire fan unit with same, similar or aftermarket (in most instances, the most cost efective method, over trying to replace just fan motor).
C) The connector that plugs into the electric fan has melted. This is/was a common problem w/ the 94/95 5.0 electric fans. Check the connector, pull it off the fan and check for any melting/burns or cracks on the actual male connector and for any damages at the female socket on the back of fan. There was a fix kit available through Ford which contained a new connector and instructions to fix. I do not believe there was ever a recall, but I think there was a TSB which outlined the problem as well as the correct method to fix & proper part #'s for any parts needed.
D) Easiest to check - blown fuse. If the fuse blew out, there's a short causing the circuit to pop a fuse. Check wiring, connector at fan, etc.
1994 Cobra coupe SVT #0013, 2011 Genesis Coupe