If things were working when you got the Jeep and only just started doing this then it is unlikely it is related to the engine swap. The only way I see it being possible to be related to the engine swap is if they did a poor job of reconnecting a ground between the engine and the chassis.
Given the problems you are describing I would be more inclined to suspect a ground problem in the interior of the vehicle. I think there is one behind the panel to the left of the driver's footwell.
It will be worth it to get access to a Factory Service Manual. I think you can access them online for less than $20 (Dinosaur that I am I have always bought old greasy ones off ebay). Find a way to study the wiring diagrams that include the accessories which are acting up and then figure out which ground connection(s) is(are) common to them. The ground connections will probably be labelled as G7 or G15 or something like that. There will be another place in the manual where it will tell you the locations of G7, G14 and all other grounds. Doing your research this way will save you some discomfort compared to trying to follow all the wires under the dash and behind the interior panels, and while there is a learning curve with either system, this one's learning curve will transfer to more situations. And it is generally better to be able to study the problem from the comfort of a nice seat inside as opposed to twisted into a pretzel under the dash, outside, in the cold. While it is snowing. And probably dark.
Oh, and count your blessings you have a Jeep and not a Land Rover. You could be dealing with Lucas, "the prince of darkness". Elsewhere you have noted that you are not particularly mechanically inclined, so you may not be as aware of Lucas Electric. Just know that Lucas headlight switches have three positions: Off, Dim and Flicker. And the reason the British drink warm beer is that Lucas builds their refrigerators. Yes, life has its challenges, but there is always someone who is worse off.