[Number 3]

FMVSS 114 makes it difficult and impractical. Read FMVSS 102 and 114 and see how many times the word "park" is used.

Essentially it's very easy to know if a vehicle is in neutral. Gear indicators are fairly common. You could also ensure with an EPB that the vehicle is also in a state that it can't roll away in neutral. What you would effectively need is a mechanical lockout of the gear shift lever such that while remotely started the vehicle CANNOT be put in a forward or reverse gear.

It's possible, but not practical to have remote start with a manual transmission.

You have to be able to LOCK the vehicle in PARK. And even though I believe some cars with E-shift transmissions use the park brake as a PARK condition, you still cannot put a vehicle into gear unless you have started the propulsion system unless you have the key in the ignition and on or you have a keyless fob inside the vehicle and have pushed the start button. Only then can you select a gear and even then to pull or move the vehicle from PARK you also need to have your foot on the brake (Brake Transmission Shift Interlock - BTSI).

So you essentially have to create a PARK condition for the manual transmission.

It's also not quite clear whether you would also need to have BTSI with the shift lever locked out. I believe this would be the case for a manual as well.

And keep in mind, just because you can buy it in the aftermarket doesn't mean an OEM can do it. You can make your car as unsafe as you are willing to do. An OEM can't.