I don't think my account's been compromised yet, since i recently updated my password. So far, none of my friends on Facebook have not seen any changes or differences in my info/page (checked my dad's facebook profile to check my profile). But when i signed in 3 days ago, I got this message:

I have a cellphone, but my plan/phone does not allow SMS (so i think) but can send/receive text messages. I clicked on
Add Your Phone, and filled out the information...

After fumbling around my cellphone to learn how to text, i sent a text message like i was asked to and clicked
Next.

As I never received a confirmation code via response text to my phone in 3 days, I figured either my phone sucks or something is very fishy about Facebook.

So i tried again, using a different method:
Step 1: Instead of selecting a Mobile carrier, i selected the
*My mobile service provider isn't listed link, which gave me the next window...

Clicked on
View popup to add my number 
Have not received a code yet today - sent a text again at 8 this morning and it is now 7pm. Having no Confirm code or any response texts from Facebook, I clicked on the
Never got your confirmation code? Let us know! link, I get the following...

...which wants me to sign in, cycling back through everything i just went through. As I did not want to activate Facebook Text Messages in the first place, this seems like a waste of my time and a hassle, because I cannot get into Facebook to change my settings