Can I retrieve my Lightspeed Menu by API? And can I post orders from API to my Lightspeed POS?

I am trying to figure out whether Deliverect is the right tool for me. I'll be building an app that retrieves the menu from our Lightspeed K-series POS. And also that would allow to order through the app and the order would appear in the Lightspeed POS.

So the following I would like to understand

can I get the menu from Lightspeed to be shown on my app through the Deliverect API?
can I then send orders (+ capture payments) through the Deliverect API to the Lightspeed POS?
would we be able to get order updates in-app?

Thank you so much for the help!