Can using the wrong power supply slow my computer down?

Many Dell laptops are able to use 65, 90, and 130w power supplies, but they will adjust performance accordingly. Dell Support article 12174 (KB 168345) notes:

The Dell Universal Auto/Air Laptop Adapter is a 65-watt power adapter. Dell recommends that you use a 90-watt adapter with your portable system. Using a 65-watt power adapter will not harm your system, but will cause slower performance.

Specific performance throttling will vary depending on your CPU, chipset, and GPU, but overall every component will be slowed down to afford enough power to charge the battery and operate simultaneously. Laptops that require more than 65w minimum (Precision workstation class laptops, for example) will simply refuse to charge when a 65w adapter is plugged in.

If you can't help it and need to use this specific underpowered power adapter but don't want to pretty much end up with a useless brick due to a severely throttled CPU, I just figured out the way to make it go to the full speed.

Pretty much what you need to do is reboot into the BIOS and in Performance settings disable SpeedStep and C states (I'm not sure which one did it, maybe SpeedStep alone is enough, maybe both).

After that, my CPU stopped locking to 800MHz and performance is as good as ever. Funny enough, the battery is actually charging and not depleting slowly, as I was afraid it might.

As for the concern that the power adapter will overheat and potentially cause fire because it'll try to overexert itself, I don't see it as an issue here myself. It's warm, but not warmer than usual, and not remotely hot.