how long will MacBook be able to use messages when phone is powered off?

If SMS / MMS text messages you compose on your Mac are in fact being sent, then your iPhone is not powered down. A Mac is not a phone and cannot send text messages on its own.

On the other hand if those messages are using Apple's iMessage service, you don't need an iPhone. Your Mac can send them on its own.

Text messages are green, iMessages are blue.

Use Messages on your Mac - Apple Support

1Turbo_slug_forever Said:

"how long will MacBook be able to use messages when phone is powered off?: My phone is unusable, and logged out of iTunes, so i've powered it off... but i'm still using my MacBook messages with no problem. Firstly, how? Secondly, how long will that last?"

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Your iPhone is Unusable? Ho so?

Troubleshooting SMS Messages Going Through:

You have set up and are using SMS messages on your Mac. This is going through your Carrier, while your Mac connected to the Internet. It should last until you unpair this iPhone from your Apple ID.

1. Go Here: Set up iPhone to Get SMS Messages on Mac - Apple Support
2. As it Reads: "Important: To receive and send SMS and MMS messages on your Mac, your iPhone must have iOS 8.1 or later, and your iPhone and Mac must be signed in to iMessage using the same Apple ID."

1Turbo_slug_forever Said:

“how long will MacBook be able to use messages when phone is powered off?: […]I dopped my phone a couple times and messed the screen. The phone kept putting in the wrong password and trying to call emergency, couldn't do much with it”

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Then get your iPhone serviced, ASAP. If you can’t power off, then it will keep performing like this, until the battery charge runs out.

It's Time for a New Screen:

Your iPhone Screen has be highly damaged, and it may be overheating, as a result.

Getting a New iPhone Screen:

Contact Apple, and setup a Genius Bar Appointment or see an AASP (Apple Authorized Service Provider) in your local area. Be wary as to where you get this item, ask you may get an error of an ungenuine Mac screen. So, to avoid this continual message, it is best to have an Apple or an AASP replace the battery. So, where to get a new battery:

A. Apple Contact Info:

• Contact Us - Choose Locations
• Proceed from there, as necessary
• Why the Wait: Phone calls are taking a bit to go through at the moment, due to lots of calls. With the Coronavirus Pandemic, many are at home at the moment, with much time on their hands to contact Apple. So, just stay on the line, and you will get through :) 

B. Contact an AASP: 

1. Go Here: Find Locations - Apple Authorized Reseller
2. Click: Service & Support
3. Enter: your location information
4. See: if there is an AASP nearby
5. Contact: an AASP that shows up, and find out more about the services that they offer to fix the battery