Quote Quoting cannonfodder
1. I gave verbal notice and not written. But I gave 6 weeks notice. Will this have any merit in small claims court?
Does your lease require written notice?

Quote Quoting cannonfodder
2. The fact that the form didn't have 30 days written in the blank spot (even though its probably in my lease), is this a factor? Are they obligated to either fill that in or verbally remind me?
The requirement of a month's notice comes from California law, not from their lease form, so I doubt that you could make anything of the space being blank. Some tenants may want to give longer than 30 days notice, for example.

Quote Quoting cannonfodder
3. If I am obligated to pay rent until the 15th, is it a continuation of my existing lease or do I have to pay market rate?
It would normally be at your regular rental rate. Does the lease provide for any sort of increase?