Learn Italian: Stavi riposando, adesso corri!

Commands for tu (informal "you") end in -a only for verbs that end in -are (like mangiare becomes mangia!). Because correre (to run) is an -ere verb, its tu command ends in -i.

Corri is also the regular present tense for "you run". Are they exactly the same word?

Yes! For -ere and -ire verbs, the informal tu command is identical to the regular present tense. You can tell it is a command here because of the exclamation mark and the context of telling someone what to do.

What is the grammar behind stavi riposando?

This is the past continuous tense, used to say what you were doing at a specific moment in the past. It is built by combining the imperfect tense of stare (here, stavi for "you were") with the gerund of the main verb (riposando for "resting").

Could I just say riposavi instead of stavi riposando?