My coop is from the 1970s and has fairly strict electrical requirements due to the old wiring.
The best cure for old wiring is AFCI breakers. They listen to the power line for the "sound of arcing" (almost literally; if you've ever hooked up speakers with the power on or had a bad wire in a headphone cable, that crinkle-crunch sound is the sound of arcing).
This will catch the majority of problems we worry about in old wiring. GFCI also has some modest ability to help, but AFCI is the critical tech.
For retrofits Code allows it to be retrofitted as a receptacle at the first outlet in the string, although this fails to protect the home-run from the panel. However if you have no requirement for AFCI whatsoever, you are free to put it anywhere you please.
If the issue is aluminum wiring relax - there's a strategy for making those safe. AFCIs help, but use of modern certified CO-ALR receptacles and switches ("R" for revised unlike the 1970s); using a torque screwdriver to set torques properly (unlike what was done in the 1970s), and "AlumiConn" or "MAC Block" splices
For my stove/oven, I need to find something with a maximum power rating of 5 amps or less.
That will be defined by the nameplate on the appliance, which will state the number of amps it draws. No other figure matters.
If you're at an appliance shop, just search the bottom/back of the appliance for the nameplate.
If you see VA and not amps, divide by system voltage (i.e. 120V) to get amps.
In addition, the dishwasher is hardwired to a dedicated circuit. Has anyone replaced a hardwired dishwasher? Does it make sense to do, or better to have an electrician just install an outlet?
If you add a dishwasher receptacle, you will need to achieve a strong understanding of GFCI. It must be a plain receptacle, but it must be GFCI Protected which means the test/reset button must be somewhere else.
Also, Code requires a disconnect switch for hardwired dishwashers now.
One clever hack I've seen (well, I've invented lol) is to have an extra gang at the disposal switch, and install a GFCI "switch" next to the disposal switch, which provides both GFCI and disconnect to the dishwasher. When it's next to regular switches, the bizarro form-factor makes people ignore it, which is just right.