Is "in" necessary? Can the bare ablative do the job?
In is necessary. A bare ablative can do various jobs, but not this one.
What's wrong with Marcus natare in piscina?
"Natare" is the infinitive form: "to swim." You need to conjugate it for the subject Marcus, which is third person singular. The third person singular form is "natat."
What's wrong with "Marcus in stagno natat"?
with macron, Mārcus in piscīnā natat.