Are contractors and architects required by law for restaurant build out?

You should check your lease. Unless you own the building, your landlord will have requirements that must be met, and sometimes that will require you to have not only the contractor and architect...but the specific contractors and architects that the landlord uses.

On the OTHERHAND ..if you are leasing...if you haven't signed the lease yet, you can negotiate with the landlord to do some of these things for you. At no charge. Because they NEED a tenant.

In this day and age, landlords are rather desperate for paying tenants so see if you can get them to get and PAY their OWN PEOPLE to do the work for you.

Seriously you have enough on your plate without having to worry about injuring yourself doing a build out before you open your business!

If all the permits are acquired and the structure is up to code, it's fine. 

No. But it has to pass inspection and one or both may save you some time/steps.

You are very likely going to have to have the building dept.'s approval to build.  That requires an architect to draft and submit the plans.  If you can build to code, go ahead and do it yourself, but you will need the inspector to inspect and approve as you go.

You are not required to hire an architect.

Unless you are a licensed contractor, you will not be able to do any work that needs to be performed by licensed contractors/plumbers/electricians.