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iMessage uses data if you are trying to communicate with another iPhone user. There's no easy way around that. Any non-iPhone recipients and iMessage will send as a simple SMS/text message though it will require the cellular connection for that to work. If you have cellular data shut off, iMessage may try send as a text message but not likely for the first few tries if iMessage knows the recipient has an iPhone. In that instance the sending and receiving party will need cellular connectivity (no data) since that is how text messages are sent and received. Any pictures or iMessage stickers, etc., will require data/wifi.
If your iPhone 6 is the one on talk and text, whatever you do with it won't have any impact on the party receiving the message. If the recipient iPhone user is on cellular, wifi or has the phone off, you'd still be able to send when your phone is on wifi. They won't have to shut wifi off for it to work. If messages are sent as text/SMS, a cellular connection is needed as they won't go over wireless.
It appears that the iPhone does not work on a strictly talk and text plan.
It will, but you have to never use iMessage. You would need to turn off iMessage on your iPhone, removing any contact information linked to your Apple ID, and also delete any existing conversations with others. You can't smoothly use iMessage at times and not at others, as Apple's iMessaging servers think you have connectivity.
The Send as SMS toggle works in some instances, but not all, causing delays in message sending, so not using iMessage is the better option if you do not have cellular data.
You also need to ensure you do not have iMessage running on any other devices, else the iMessage server will preferentially send there.