No, batteries are larger. People tend to use the trunks for batteries, or convert pickups and put them in the beds.
> Will this have an adverse impact on vehicle dynamics?
It can, which most people deal with by placing the batteries carefully to maintain the same balance as before.
> How are you going to manage charging these things?
Most people put the charging plug where the gas cap was.
> What happens if the battery pack ruptures? Is safety even a concern?
Same as if your engine explodes. Safety is a concern in any car. Problems can happen in any car. Most DIY EVs put a cutoff switch, or even a main line you can literally cut right next to the driver as a final safety net in case of extreme emergencies. Better to kill the car than a person.
Does the fuel gauge show battery life or is it now useless?
Most people replace the gauges with new ones more applicable to the new information they'll need.
I know you had other questions, but it has been 10 years since I dabbling this space, and I don't remember every detail. But yes, there absolutely are new problems to solve. And people have been solving them for 20+ years now. There are books written on it, so if you truly want to know the answers, go read some of the books. Most of your questions either have easy answers, or are just a matter of making a choice between a few options.
The hard part is not putting together a working EV system. Most people's hardest task was mounting the motor to their transmission, because it often meant a custom designed, and custom machined mounting plate.
So again, you are correct that it is more than an engine swap, but not to the scale you are describing.