Do I have to bring my own locks? If so, why? If so, how many should I bring?

Yes, you have to bring your own locks.

At the sale they will unlock the company's lock and cut the former locker renter's lock. Sometimes the former lkr renter's lock will have already been cut off.

Once you buy the locker your lock goes on to protect your investment. Sometimes they will put their lock on too until you have paid, then they will take theirs off.

You should bring 3 or 4 locks but might only need to carry one or two on your person with the rest in your vehicle. Chances are you are not going to be buying more than one or two at a facility.

Yes, you will need to bring your own locks with you to the storage auction. As soon as the auctioneer says sold, the contents of the storage unit are legally yours. You are required to immediately secure your merchandise because the storage facility does not want to be held responsible in case something comes up missing.

In the beginning, while you're unsure whether the storage auction business is right for you, 1-3 common locks may be sufficient. Once you're committed, I recommend that you invest in several disc locks that are keyed the same. Having locks that are keyed the same will save you time and frustration. You can usually find these on eBay for $4-6 each. If you forget to bring a lock, most storage facilities sell them; however, they are usually overpriced. 

When I was buying full time, I kept about ten locks with me; 3 on my person and several in my vehicle. Under current storage auction conditions, this may seem excessive; however, it doesn't hurt to be over prepared. How many locks you will need depends on how many lockers you could realistically purchase & move in a given week.

 I simply keep 5-6 locks in my trunk.  I pick them up at garage and estate sales for $0.50-$1.

I carry in two.  One cylinder style which i prefer and two smaller 'normal' style. 

One, some of the facilities the cylinder style doesn't fit.

Two, a good 10% of the auctions a newbie doesn't bring a lock and I'll sell them one.
Even if they don't buy.  As soon as I overhear the whispered "we are suppose to bring a lock?"  I step up.
Pays he days gas at least.....

I personally like the cylinder locks.  They are harder to break but mainly because the key hole is on front and easier IMO.

I also have a red tag, strip of cloth with a brass ring in it, that I hang on my lock.
I've spent way to many times forgetting where my locker is so the "flag" marks it.

And yes, I'm an idiot sometimes.