My daughter's father and I have not been together for almost 3 years and we are still arguing over my daughter and who should do what. I have her most of the time and he takes her Wed night, Sunday afternoon and every other Saturday(day and overnight). We are both in our early 20's. My questions are, is it fair to expect him to pick her up and drop her off when it is his days? I feel that since I have her most days, if he wants to see her he can pick her up.
Also I have been dating someone for 1 1/2 years and her father is still saying unnecessary things about him and questioning his actions with my daughter and wants to know why we go to his parents house, if he has moved in with us (my daughter and I live by ourselves), how I can afford certain things, is he paying for them? I feel that while I understand that he is not around her and another man is, I certainly do not owe him all the answers to his questions. He is also dating someone (recently new) and I have not once questioned him in regards to his girlfriend and my daughter. Do I owe him explanations of what we are doing if it is not endangering my daughter?
We try to be civil towards each other but once in awhile we get angry and everything comes up again. Is it always going to be like this?

You should let him know first of all that what you do and how you live is none of his business as far as your child I have a stepson and we have somewhat of the same visation as your ex and we always meet his mother at a location that is in the middle of where she lives and where we live which I think is the bast way to do it so that we don't have to interfere with her home or her business and she can't interfere with our home or business.
Make the pick ups and drop offs very quick so that it won't cause controversy if he insist on asking questions let him know you are busy and in a hurry and that you will meet him at the same location for the next pick up and drop off.

My ex and I meet at a point that it half way (time wise) between our homes for every exchange. While in my state it is common for the non-custodial parent to pick up and drop off the child, I didn't want her dad at my home and our exchanges went much more smoothly if they were done in a public location. You certainly do not owe your ex any explanations about your personal life whatsoever. He only needs to be informed about things going on with your daughter. He has no right to demand you tell him how you can afford anything. Also, you may want to consider changing your weekends to each having her every other weekend... I know that doesn't sound ideal now, but when she gets older it will make things much easier, especially if you want to travel over the weekends. Every other weekend from Friday night to Sunday night and one weeknight for three to five hours, alternating holidays and 2 weeks in the summer is a typical agreement where I live if the parents have primary and partial physical custody of the child.

Ideally, it would be much better for myself if her father took her from Friday night through Sunday night every other weekend, however, and I quote he said "he needs to have a life". And actually he called me yesterday and was angry because my daughter had a scratch on his knee and wanted to know where it came from. I feel that he was just trying to start something but I remained calm and explained that she fell.

I think that the idea of meeting in a public place is good. I think that we should also be the only people at the pick up/drop off or am I just being picky now?

If you want to modify the visitation agreement, you will either have to go back to the court or get his approval.

As to whether this will go on forever, I suspect that it will unless he grows up and moves on with his life.

You DO need to inform him that your personal life is no longer any of his business, however, that's not 100% correct since anything that affects your daughter is, at least partially, his business.

There are no hard and fast rules here. Unless something is spelled out in the divorce/custody agreement, then its subject to negotiation between the parties.

He sounds like a pain in the... anyway, I don't think it is being picky to make sure your child is being picked up by someone in particular. I had similar concerns when my ex and I split and named all the people allowed to participate in custody exchanges specifically in our custody agreement. That way he couldn't send some stranger or his new g/f of two days to pick up our daughter. It worked out well. It will be a long time before the two of you are both completely over whatever went wrong between you, so anger will be there and unfortunately, now that you've parted the only thing left to get petty about is your child. So please be expecting him to continue behaving badly, but don't follow his lead. Keep your head up and stay calm. When he realizes he isn't getting under your skin this will stop and you can both focus on your daughter's needs.

I am divorced and the court determined who would do the dropping off and picking up. I would double check your divorce decree and see if it has been stipulated. If you were never married or your decree does not address the matter, see an attorney to draw up a legal visitation arrangement that puts all of this in writing. Most states have guidelines and if you and your child's father can agree to just follow the guildelines, you can avoid becoming contentious about things.

YOu might be able to difuse his questions/comments about your boyfriend by simply having a conversation with him something like this:

"I know you are concerned about our daughter being around my boyfriend and may worry that you will be replaced in her life. I want to reassure you know that while I will not be sharing details of my personal life with you, I will always value your roll as our daughter's father and will not permit any man in my life to replace you. I will also not let any man who does not treat her well to be a part of her life, or mine. That said, you should not be commenting on who I date to our child - it is confusing for her and puts her in the middle of an adult matter. I will extend the same courtesy - if I have any concerns about your girlfriend, I will bring them to you when our daughter is not present."