A driver's license is also a reliable form of identification because it is issued by the government and is a photo ID, not just a card with a name. Make sure you have a "non-operator's license" issued by the DMV so that you have a form of ID when applying. It would depend on the employer, but you can always apply without all of the listed credentials. But they very well may put you at the bottom of their list.
You could apply to the jobs despite not having the driver's license. However, chances of getting an opportunity in the company are limited. The requirement must be necessary if the employer mentioned it during the application process.