How can I use my Samsung S4 phone functionality from my Asus Nexus 7 tablet?
It's simple. Download the WhatsApp Messenger App on to your tablet. It's free for a whole year, then you pay $1/year to keep using it.

By default, WhatsApp isn't compatible with tablets, but there is a work-around for that...

...Right Here
You can also try Line, which is another messenging app.

Also...TextPlus has the least amount of work to setup (it's compatible with tablets), but it allows you to send texts and make calls. Though it's not as good as WhatsApp or Line

I've also tried MightyText, which works just fine. Not sure why it won't work for your phone...