Does he want to cheat or leave?

I've seen so many supportive people on here, giving wonderful words of wisdom. So here it goes, story and all. I'm sorry it's going to be long, I just need to let it all out.
When I first met my boyfriend I was young, still in high school. It was senior year and all was well. I met him when he worked one day (retail), and we exchanged numbers and things went from there. After I graduated, that's when we started hanging out more and more in person. As time went by, we eventually moved in together and we now have a one year old baby. Throughout my pregnancy he was great, but when I hit around 5 months he started working more and more. Like he should've got off at 10, but wouldn't get off until 12-1 in the morning. Every single night! Then he'd go hang out with his friend "we will be outside", an hour passes I look out the window and he's not even there! They're gone and he never even told me. He still does this, still often too.
So fast forward a few more months, I have our baby. I'm too out of it to even function, but I still care for our baby and breastfeed. Changing the diapers and clothes, doing it all because he's "tired", but I'm the one who was so far out of it I didn't even remember grabbing my baby to feed her, I thought she manically appeared on my boob! So far, I never thought a thing of it. I thought he was on Facebook or a phone game. Even texting his best guy friend would've been great! I didn't care at that point. I only cared about our daughter. So after a rough last 5 months of pregnancy, and a shockingly smooth birth we were ready to go home. Good, great right? I thought so! 
Fast forward to about 3 months after the baby was born, sex for us started going downhill. I didn't care because I was all about the baby and he was all about work. But I constantly stayed up late with her, waiting on him to come home. Sometimes he'd get in at 3 in the morning. It's retail, that's bull crap! I know his schedule, if he closes he's off at 10, 11 the latest besides in store changes. Which happened every time something new came out, not every single night! That happened for months! He'd barley text me on his break anymore, but I'd still send him pictures of our baby and the new things she done that day. Cute right?
So many months after that, our baby was around 6 months. I started seeing texts from a girl, "she's just a friend asking about a job". Yeah, that's why it was late at night with a 💕 at the end? For a job? Lies! And a whole lot more with this girl. His old phone he used a while, then gave it to our baby to play with. She openened everything! That's when I seen a message from an unknown name, if was his ex. They had messages from around the time we first met. He told her he'd never care for anyone who flirted with him and she sent him a pic in her bra (disgusting!). She also had a "boyfriend". Yeah, ok. After that I became suspicious of everything he done. One day we left his phone so I went through it. Something told me to do it, and oh what I found! He texted another girl saying "I love you too". That's not what aggravated me though, what aggravated me is after I confronted him about it he goes "that's my best friends ex, she's like that with everyone so I said it back". If he had respect for this relationship he would've told her to back off, he has a family now. He also hung out with a different girl on break, that's why he never texted me. Another thing I found, the night before we left the hospital while I was asleep, he texted a whole different girl sayin. "You can meet (my) baby anytime! Whenever you come here!". So a few months later around my birthday, he let go of my hand to hug some b**** he "worked with", though I've never seen her! At Valentine's Day he got cookies from another girl he worked with (I had a bad vibe from her from the start". Heart shaped cookies with a heart shaped note with his name on it. "They're for us" he claimed. Ok sure. So a couple days later and he threw away the cookies (they were green and tasted horrible!). Claiming he threw the note away too. I found it a day later looking for the baby's teething gel! It was under my magazine, under it! Guess what the note said? "I'm going to miss you, you're my fav person ever! Go get em tiger! ;) come back to see ME!". B**** no! He will not come back to see you! But he still texts her, he texts them all.
I recently started talking with an ex (his) about all of this. She told me he's sketchy, he's a manipulative and compulsive liar. He's very good at lying, they barley had sex (like us). A whole lot of things. I brought up his "best friends ex he said I love you too". She told me that was his ex to start with. She dumped him for his friend and eventually dumped his friend for another guy. He follows her on instagram and they're friends on Facebook. He doesn't know I know she's his ex. He has the other girl too! The bra sending ex, on his Facebook! Probably on instagram too. He likes all the girls' selfies, never any with their boyfriends! He talks to girls 24/7, but I can barley talk to my mom without him jumping down my throat about how I'm "texting other guys". He told me I can't be friends with my ex, but he's friends with his?! BS! I don't know what to do. I feel like he's cheating! If he's not foo it physically then he's for sure doing it emotionally! I'm trying to make it work for the baby, but I can't keep doing this. Is he cheating, or isn't he?