When you are texting a higher rank, do you type out their rank?

Like with any correspondence you should start it out with addressing them by their rank. You don't need to use it over and over in every single text sent back and forth during the conversation. That's just extra. But definitely open the conversation with addressing them by their rank

I use their rank abbreviation. Always. But, that's just me.

I would start out with the correct form of address. You can use the common Service abbreviations for the rank, such as CPT Jones or SFC Smith. After than continue your text. If you happen to be in a joint service organization, make sure to use the proper Service abbreviation for the person to whom you're texting.