Does Apple Cash start me with a credit limit that they offer me like a regular credit card would ?

What is the name on the card? Does it have a symbol like a Visa, MasterCard, American Express, Discover?

Apple Cash is a prepaid debit card and funds need to be transferred to the card.

Green Dot Bank is the bank that services Apple Cash Accounts.

Apple Pay is a method of transferring data in a secure method when you pay for a service or a product. Again, it would have no credit limit.

The only consumer Apple credit instrument is Apple Card MasterCard, issued and serviced by Goldman Sachs Bank.

No, Apple Cash is a prepaid debit card and a service of Apple in conjunction with Green Dot Bank. You must fund Apple Cash with a debit card. Please review the Apple support article I linked below.

Add money to Apple Cash - Apple Support

You are correct. You have to put money in your Apple Cash in order to use it. Can we assume you know the difference between the Apple Cash card and the Apple Card Mastercard credit card. They are two different things.

The only way Apple puts money into your Apple Cash account is through the Daily Cash Back rewards by using your Apple Card credit card.