How to transfer text messages?

I had an iPhone 4, and got an iPhone 5s about 2 months ago.

I want to get my old text messages off of my old phone and onto my new one WITHOUT deleting the ones from the past 2 months, is this possible?

I want my old texts because I want to have the texts from when my boyfriend and I started to date because they are special to me.

I don't have iCloud settings turned on, but my iPhone 5 keeps telling me my storage is full?

I keep getting a message popping up telling me my storage is full but when I go into my iCloud settings, everything is turned off - nothing is supposed to save to iCloud, and I don't have backups turned on. I have no idea why it keeps insisting I have no storage space when from what I can tell, nothing is saved on iCloud. I'm not sure if this has any effect on the other functions of my phone, but things do seem to be running slower and some apps don't seem to be running correctly, so I feel like something must be off and I can't figure out what or how to fix it.

IPhone's internet will not work without Wi-Fi?

My internet typically works with and without Wi-Fi. If I left the house, the Wi-Fi signal icon would be replaced by a 4G icon or an LET icon. But recently, my internet (whether it be 4G or LET) just stopped working when I'm not connected to Wi-Fi. It has happened before and I've reset my phone to fix the problem. But now, when I reset my phone, it still won't work. It's becoming very annoying and I have no idea what to do. Could anybody help? It's an iPhone 5S if that helps anything. I also got it October 2014.

Is there anyone living today who has never had their picture taken?

Is there anyone living today, who has never had their picture taken? At first I would think there would have to be a few, but after thinking about it for a while, it seems like people in just about every single person even in developing countries, would have to at least once to have traveled to the capital city of their country, and had their picture taken in some way, perhaps unwittingly by a tourist or sightseer on their camera or iPhone, or perhaps they paid a photographer to take it at whatever landmark. I think it may be possible that there's no one living today who has never had a picture taken of them. What do you think?

WHAT US CARRIERS WORK IN MEXICO?

Okay so I live in Arizona and my father is in Mexico he has a Mexican company called a movistar and I'm over here trying to find him a phone that uses a sim card so he can use it in Mexico for him to Call us. Do you guys have any idea which carriers what work with Movistar? & what phones? Also, can I connect a us iPhone to a Movistar?

What should I put in a giveaway?

So there are all these people on Instagram that are doing giveaways and I want to do one too but I have no idea what to give away! What do people like? Everyone else has things like iPhone 5s, Eos, Babylips, but i don't know what else I could do.

IPhone 5s keeps turning itself off and on when I wake/sleep the device?

This just started today, but each time I wake my iPhone it goes through a process of trying to turn itself off, me pressing cancel, the screen turning off, and then it turning back on seconds later and then it's completely fine. The process happens all over again when I make my phone sleep again. It only happens when I press the power button but I've read that it might be something else. Any suggestions?

Why do i have to enter my password for my itunes account every time i go into my music on my iphone?

Every time i open my music app on my iphone 5c it pops up a box telling me to sign in to the itunes store. When i click cancel it keeps popping up until i type my password. It's been happening for about 3 days now and it won't stop happening. Is there any reason for this to be happening? If so, is there a way to stop it from happening? It's really obnoxious having to type my password every time i want to listen to music.

Is this a scam? Craigslists?

I put my iphone 4s for sell and within a few minutes received a text from a new York number "I'm in texas" claiming they were interested in my.phone and wanted to buy it but they were "Working" blah blah so i blew it off then i received about 2 more text from other out of state numbers kinda the same thing they were interested but working this this and that. Thats a scam right? I put local buyers only. If so how does this scam work? Has anyone here ever been scammed on Craigslist? I'm curious and would like some feedback as this is my first time using Craigslist… Thanks