Yes you may do a complete reinstall using the same product key as your 64-bit. Make sure you have that key - it may be on the bottom of your laptop or you can use a freeware product like SIW (Find it in our
freeware DB) to look it up on your current system.
If your laptop has more than 3GB of RAM/memory then anything above 3.25GB will be wasted with 32-bit (it cannot be addressed so it is not used). In fact, unless you only have 1GB of RAM or some other hardware or software reason to go with 32-bit, it is highly advisable to stay with 64-bit.
You might check out
THIS post if you do not have the Home Premium 32-bit disks.
And yes, you should download as many of the 32-bit drivers for your machine as you can find prior to the new install.