I have an ipad 2 with a cell number. I do not have a cell phone. I would like to receive messages on my ipad when I do not have a wifi connection. How do I do that?

You should totally be able to get messages over the cell network. They won't be SMS messages, but iMessages sent to your Apple ID should still be received.

iMessage requires an internet connection, but it does not care if its cellular or wifi.

You cannot use the cell number assigned to your iPad to receive messages however.

Make sure iMessages is turned on in Settings->Cellular->Use Cellular Data For.

Use Messages on your iPhone, iPad, or iPod touch - Apple Support

Yes, Apple's free internet messaging service, iMessage, will work over any internet connection - wifi or a cellular data connection. The iPad cell phone number has nothing to do with that at all and is used solely by your iPad cellular data service provider for billing purposes.

An iPad cannot natively receive or send SMS/MMS texts since those require a cellular telephone voice channel connection, which an iPad is not capable of.

If paired with an iPhone using iOS continuity features, an iPad can piggy-back on the iPhone's voice connection to send and receive SMS texts (but to use, both the iPad and iPhone must be on the same wifi network so they can connect).

you can't

you can send and receive iMessages and if you have an iPhone it can be used to send sms from the iPad but the iPad itself can't send sms or mms's