To answer your questions:
How can I be sure that my laptop is compatible with 64-bit Windows 7?
Your processor supports the "EM64T" instruction set, so at a fundamental level, it is compatible with Windows 7 64-bit. The real question is whether it will run optimally on 64-bit. By optimally, I mean, will it only run the Microsoft built-in drivers, or are there 64-bit native drivers available for the customized hardware.
On the Dell website, I only see drivers for Windows 7 32-bit. Will Windows 7 64-bit supply its own drivers for my laptop, or will I be unable to use the 64-bit version due to the unavailability of 64-bit drivers from Dell?
As you can see from the page linked to by Matthew Williams' answer, it appears that 64-bit drivers do exist for your computer, contrary to what you said. Even without these drivers, though, Windows 7 should at least install and boot up to the desktop, though you may not be able to take advantage of all features/buttons or get the best graphical performance in the absence of 64-bit drivers. That's not a problem for you, though, as the drivers seem to be there.
If I try to install 32-bit drivers on Windows 7 64-bit, will the 32-bit drivers work?
No. It is not possible to make 32-bit drivers work on a 64-bit operating system.