Prepare Voice & Body for being a Musical Lead

I have just been cast as a female lead (adult, Mezzo Soprano) in my local theater group's musical production! I have over 100 lines and a couple of solo songs. Imposter syndrome is setting in!

I know of techniques for warming up my voice, but what can I start doing now to prepare to PROJECT my voice (acting & singing) for 3 hours during the show run?

I am nervous because this is my first time being cast in a role, and when I've gone to shows/concerts, my voice is usually hoarse the next day.

I'm also overweight and would like to know what sort of exercise other Leads tend to take up! Would running a mile a day while singing be reasonable or just silly?