How can I save text messages to my Mac and will that reduce "Other" in storage?

I have hundreds (or more) of text messages on my iPhone 5 that for personal reasons, I want to save. There are far too many to do screenshots. I want to save them to my MacBook Pro Retina in a readable and printable format. The reason is that I read that text messages can cause the "Other" storage to be higher. My "Other" is over 6 GB on a 16 GB iphone. Therefore I want to save texts, print them, and delete from phone.

First question: Is it true that text messages contribute to the size of "Other"?

Second question: How can I save texts to Mac in readable format so they could be printed?

Third question: How in the world do I delete all these texts from my iPhone efficiently? Is there a way to "mass delete"?

When you are answering this, perhaps it is noteworthy that:

(a) I've had an iPhone since a 3G in 2009, and the texts I want to save have been accumulating since then.

(b) My "Other" has gradually gotten larger over the years.

(c) I sync with itunes regularly.

(d) I've never had any problems with an iphone or with my data.

(e) I've restored from backup only three times, when I upgraded to the iphone 4, 4S, and 5.

I want to get this "Other" cleared up before I upgrade to the iphone 5S.

Thank you.