Also - to add in...Did you check the condition of the Battery?
It's cables?
(Oh sure they may look good, I mean look closely)
IF you have not had any service done to the battery - best to wear gloves to protect yourself - or have it towed to a mechanic that can handle the acid and disposal of that old battery.
It's not the best way to approach a mess like this is to presume to just drop in a new starter - the starter systems in these vehicles are quite different from the older days. To have them fail - means you'll have to tear apart some pretty big areas of wiring and parts to drop the starter and swap in a new one - but even doing that is no guarantee let alone you've re-hooked up all the parts and wires to make it work.
The PCM controls the Starter system - you just have to tell it to start, using the Key, or button - either way, the PCM checks the system, and sends a "Start" signal thru Relays and the solenoid on the starter - and only cranks for so long until specific conditions are met - you'll see those wink out on the Pods as the systems "wake up" and start the car for you.
To me, the reasons "starter" doesn't work, is more closer to a bad battery and corroded cables, than to presume the starter is "bad" - there are systems the PCM controls to do that for you as a means to protect the vehicle and you from having failed systems - a bad wire though, can cause you to think that it' is a bad starter when its just a battery cable or a connection that has failed and you just need to clean the corrosion off of it and re-establish the contacts so the PCM can tell the Starter to turn over.
So, did you get a tester yet?
These threads might provide some direction to help you find quirky connectors...
https://www.fordfiesta.org/threads/body-control-modual.8227/post-20339
https://www.fordfiesta.org/threads/help.8317/post-21317
https://www.fordfiesta.org/threads/windshield-washer-issue.7786/post-25911