My 2003 V8 4runner has two issues right now.

1. Both the VSC light and the Trac Off light came on in the dashboard. What is the most common reason for this? How do I fix it?

2. My alarm doesn't work anymore and I was told maybe one of my fuse is messed up. Does anyone know what the fuse # and amps is for the oem security alarm? Is the fuse box underneath the dashboard or is it in the engine bay. There's two of them. Can someone show me the diagram for the fuse box? The lock and unlock button on the key fob is not working.

Your owner's manual list all of the fuses and what they are for, if you don't have a owner's manual you can download it and other documents from Toyota Owners website...

2003 Toyota 4runner Manuals & Warranties | Toyota Owners

There are 2 manuals for the 2003 depending on the manufacture date...

The fuse listings starts on page 352 in the earlier one..The fuse listings starts on page 356 in the other one..

Both the VSC light and the Trac Off lights on my '04 V8 4runner have been on for a few years now and I plan on leaving it that way.
In my case, I was checking the cause of a CEL using an older cheap scan tool and it was the scan tool that tripped the VSC light and the Trac Off lights on. If you have a scan tool capable of reading C codes it should show a C1336 code indicating that you need a Zero point recalibration.

It indicates that the traction control is off and never liked having it on to begin with. Seeing how your in California however it will probably cause a problem for you when it comes to passing the emission/safety tests.
Resetting it can be done easily just google "zero point calibration" for your vehicle.

Cool. So it's no big deal. I have heard the car drives better and is a lot less annoying with the VSC and Trac off.

Yes it does. I always found it unnerving when that traction control kicked in.

I do beleive the state of California will fail your 4runner during the emissions/safety inspection for that so you will have to deal with it before your next inspection. I've gotten away with in for several years because here in Wisconsin they don't care and I've passed the emissions test twice with the VSC and Trac off lights on

There is a thread here somewhere that explains how to install a switch to allow you to turn it on or off at will.

My VSC and trac off lights pop on periodically and I have a shop scan the codes and they go off with no problems. They said it may be a computer issue of some sorts in communication but I have no problems with my VSC at all. Maybe have someone code scan them and see if they pop off with no problem.