Hi Far Side,
I identify with how you feel in many ways. I know how difficult it can be. I'd like to offer a few suggestions. For one, John 4:8 says "Draw near to God and he will draw near to you". You say you don't really pray, how can you develop a relationship with someone you don't speak to? God stands at the door and knocks, he nudges us gently and draws us to him, he whispers quietly to us with that still small voice. But many of us aren't listening, and many of us aren't talking to him (praying). God wants a relationship with us, and every relationship has to go both ways. I had a hard time with praying as well. I always thought that I had to "do certain things" in prayer. I had to be on my knees, I had to beg and plead for mercy and forgiveness and praise God over and over. Then I realized it doesn't have to be this way. God is my father. I am made in his image. And while I SHOULD praise him and I should be asking for his mercy and forgiveness, I should also be doing this in a natural way that develops a relationship with God. So now, I just talk to him like I would talk to a father, mother or best most trusted friend. I tell him my concerns and fears, when I see something beautiful or appreciate a warm summer day or the beauty of the full moon I thank him for it, I thank him for creating it, I am awed by it and grateful for it. I ask for his help when I am struggling. I ask him to help me listen for his still small voice...sometimes when I am frustrated with not hearing I ask him why he can't just yell at me so I GET IT! lol Anyways, I treat it more like a conversation throughout my day as things happen, rather than a forced "Have to get my hourly prayer session in at the start or end of my day" thing. And it feel more natural, more like a relationship, easier to do.
The other thing about prayer is that I have realized I was praying the wrong way. I used to pray like I had to beg for what I wanted or needed and there was almost an underlying expectation that I wouldn't get it because maybe it wasn't God's will. But that is not what the Bible teaches us. We are told to pray with expectation and faith in Jesus' name that we will receive what we are asking for, and believing we will receive it and that God will supply our every need. God doesn't lie. As long as you are focused on him, and what is good, he will supply your every need.
Psalm 5:3 In the morning, O Lord, you hear my voice. In the morning I lay my requests before you and wait in expectation.
Mark 11:24 Whatever things you ask when you pray, believe that you receive them, and you will have them.
I think more than anything this is a huge exercise in faith. Expecting and believing that God will answer our prayers and then just patiently waiting and TRUSTING in him to do so- that is hard work, especially when we live in a world of microwaves, fast food, and instant online banking. We often tend to give up so quickly and believe the answer was no, instead of hanging in there and trusting that God is working on it. So now when I pray for things, whenever I begin to get frustrated in waiting or questioning where it is, I try to remind myself that God is working on it. You are God's work of art. He is molding and shaping you into someone that will fit into his plan for you both now and in the future. He could have the most wonderful things in store for you, but what he may require to get you there is patience and persistence- not giving up on him and trusting that he does have a purpose for you, that he hears you and your prayers are being answered.
Now as far as you feeling lonely and without purpose, I have a couple more suggestions. First of all, if you previously spent a lot of time with your mom and now you're not because she's been busy with your dad, maybe you could try talking to her and letting her know you miss the time you spent together and perhaps you could suggest a girls night out one night a week or every second week or something. Your mom can't read your mind, and honestly so many young people your age have little to no desire to spend time with their parents and would rather be out having fun with friends or something. Maybe your mom thinks you are better off now that she's spending more time with your dad. Maybe she felt she was holding you back from spending time with other people your age or doing other things. I'm sure she has no idea how you feel and if she did she would make every effort to spend more time with you as well.
Also you could try joining a Christian meetup group or starting one of your own to make new friends and get out more. There are tons of great groups on meetup, some of which are Christian groups. I am part of a few groups myself and many times people without a vehicle will just post a message to the group on the meetup page they are interested in to pay some gas money in exchange for a ride to the activity they are interested in attending. You could even try this with volunteering. Maybe contact a volunteer organization you are interested in and let them know you'd like to volunteer but wondered if there is anyone who could help with transportation to the soup kitchen or wherever it is you are interested in volunteering.
Anyways, hang in there. Don't give up on God. I promise he hears you and he isn't giving up on you either!