Disclaimer, I was an HVAC apprentice for 2 summers in college when my grandfather still ran an HVAC company. So I'm very far from an expert but I do remember a thing or two about HVAC.
If your AC system is also 20 years old you might consider replacing the whole system if you replace the central air handler. In order to take the AC coil out of the central air handler you'll need to pump down refrigerant using a vacuum pump and then cut the copper lines near the coil. The coil then just slides out from the air handler. The problem comes in reassembly. Some coolant is always lost in the pumping down / cutting the lines so you'd need to add some more after it's all hooked up. That old style coolant R22 is not allow to be manufactured anymore so the prices continue to rise as supply decreases. That means a couple pounds of the R22 coolant could be 50% the cost of a new 140a type coolant system.
Okay that's likely an exaggeration but definitely price stuff like that out before you start chopping on your central air handler. The easiest thing you could replace if you're worried about reliability are the heating element and blower motor. Usually, though not always, you can replace the heating element and the blower motor (fan motor) without removing your A-coil. Then again replacing something like a fan motor when the current one is working fine is a waste. What is your end goal of the furnace upgrade? If efficiency, upgrade it all at once and get a more efficient AC and furnace. If peace of mind, stash some money in your high interest savings account and have a couple of local HVAC contractors in your contact list so you can find help when it finally dies on the coldest / hottest day of the year.
To your detailed questions:
1 Wiring: You'll need to wire the thermostat, might involve pulling 5 wire thermostat bundle instead of 3 or 4 wire bundles. Just depends on model. Usually the 120V connection is hard wired to a dedicated breaker. Some furnaces have plugs though. Depends on local codes.
2 AC: Likely need to cut copper lines to remove. Depends on space available. If you have room on both sides in an attic then you might be able to gently bend the copper tubing and set the A coil next to the air handler. If you cut, you must pump first. BTW trying to bend 20 year old copper pressurized with horrible-for-the-environment toxic gas is a 100% bad idea. It might work though.
3 plenum: try to get as close as you can to the existing plenum's size opening. It's usually impossible for a perfect fit. You'll make an expander / reducer out of sheet metal. Duck bill pliers and tin snips make the job easier but there are many ways to get this part done. Usually in a tight space so requires some creativity. Some seal with foil tape but I'd suggest sheet metal screws and seal seams with duct mastic.
Again if you're replacing a furnace that has the Air conditioner coil inside the air handler as one unit, it's often easier to replace the whole mess together. If you size up or size down your old A coil might not fit. Air follows the path of least resistance so if there's a gap next to your A coil in the new handler box, most of the air is just going to run right past the coil and not cool down efficiently. Full HVAC replacement is definitely hard DIY work because of the combination of systems involved. It's possible to get an understanding of electrical, gas, refrigerant, plumbing (drain lines) but here is a case where they all come together usually in an attic with limited space. So it's not like adding a ceiling fan where you flip a breaker, mount a box and twist some wires. This is something that takes much more planning.
My advice? Go down to the HVAC specialty store or start calling around. There's probably someone who can help you DIY this as a "moonlighter". You will be 100% responsible to pull permits yourself and accept all liability yourself but you can pay the moonlighter to use his/her specialty tools and experience to make the whole process easier. Unless you have a large shop already there are going to be some new tools you'll need.