A 12 V lead acid battery ranges from around 12.7 volts when fully charged down to around 12.2 at 50% (the minimum recommended charge level for typical car batteries). When starting the car, the voltage will drop below that. When the alternator is running to charge the battery it is around 14 V.
Is there any regulation or filtering on the 12 V ports on cars, or do devices plugged into them see it all--the alternator voltage when it is running, a big drop when starting, and 12.7-12.7 at other times?
There's no standardized regulation or filtering; devices typically see it all. And it's much more than the alternator voltage; a device might see transient 24V or more, and as little as 9V.
Modern chargers tend to be really forgiving, and they're often powering a device that has its own battery, so there are multiple levels of regulation between the car and the device.
On the other hand, I've used automotive adapters that do a simple DC-DC conversion with no regulation, and pass through to a barrel connector to a device that would otherwise be powered by standard alkaline disposable batteries. Those aren't nearly as robust, and I've seen devices fail or power-cycle due to undervolting.
Not necessarily, and there is way worse stuff on that power source than that. For example, you have to guard against things like “load dump” where voltage can spike up to rather high voltages momentarily (80V or so, don’t know the actual spec right now).
Chances are that a modern car has more regulation and protection between battery/alternator and the 12V plug, but you don’t usually know what, and the spec doesn’t (or at least didn’t when i looked into it) require it.
No filtering, it goes directly to the general power rails in the car, with all the noise included. Devices are responsible for filtering/protection as needed.