Social security

You can apply.  My son did as he was going to be self employed

Once I get the social security number will I have access to the Spanish healthcare immediately?

I am just about 100% certain you are not.  My son did not.

You need to at least have the offer of a job, confirmed on official paperwork with relevant reference numbers, so that you can apply for your EU Citizen Registration.  The job or offer are sufficient to prove income and health cover for that application

When you start the job and commence paying your health contributions,  you are then entitled to medical cover

Thanks again
Do you know how much are the contributions for a self employed person or is it a percentage of the income?

I understand it is a fixed amount and that fairly recently it was reduced,  from what was pretty high, to a more reasonable level.  But that is only for a limited time

If you search the Internet I am sure you will find more specific info