Can you bring your own stroller into the park ?

Yes

Depends on how wide the stroller is , if wider than 3 feet come May 1, no.

Yes but size limitations apply

If your stroller is larger than 31 inches wide and 52 inches long it wont get inside the park. Disney will rent you a stroller for $15 a day.

Yes but after May 1st it cannot be wider than 36 inches

Yes, but starting May 1st there will be restrictions on the types you can bring.