Do I need a company to publish?

No, an individual account works on both stores. A company account looks more credible on the listing and keeps the app tied to the business rather than to a person.

How long does approval take?

It varies with the store, the category and your account history, so submit well before any launch campaign. Plan for at least one rejection on a first release.

Can I publish one build to both stores?

Yes if the app is cross platform, but each store still needs its own account, signing and listing, see Native or cross platform, which should I choose? .