The best thing you can do is get lab experience, and internships. You could have a degree in biology, microbio, biochem, math, physics, chem, etc. and have an equal chance at getting into a grad school if you have had a good internship/ lab to work in.
With any science major you are able to take marine classes, but it does help to have skills outside of marine biology (e.g. math, computer science, stats) because those skills will set you apart from others who are trying to get into that same program.
Many marine ecologists use a lot of modelling so knowing how to read and write code and knowing bio stats makes you stand out against the rest.
Yup. Yes. And definitely!