Could a bull spread have zero initial cost?

You have same premium cost for options with the same delta. Two call/put options with different strike price can never have the same delta. Only a combination of a put and call or two calls/put with the same strike price will have the same initial cost.

No becuase you are buying and selling options with different strike prices.  In a bull call spread you’d be buying a call with a lower strike and selling a call with a higher strike so you would have a net expense.  A bull put spread you sell a put with a higher strike and buy a put with a lower strike so you have a net income.

No.