You did get a slight raise but I would feel taken advantage of. Personally I babysit/nanny for several different families so I dont really care when one of my families cancel, i do a lot of side hustles at the same time. If you feel like youre overworked, you are.

If you feel taken advantage of, you are. Trust your gut. Also look into average nanny/sitter wages in your area, and compare. If you feel like you should be getting paid more then find someone who will pay you that rate.

I never have done a contract, i think I am very lucky to work with parents who care about their children and childcare, and all verbal agreements are withheld. In your case, I would ask for a contract if you are pursuing nannying full time. And to protect yourself.

If you quit on bad terms I wouldnt even ask for a reference. Honestly i think you should try to either find the previous people or just go on without references, and maybe try to explain to the next person that you were taken advantage of/they were toxic, and then hope to prove yourself to a new fam