Sweetie, I am 32 and I have no idea what I am doing wrong when mine acts like this. You are not alone! You need to be firm and no-nonsense and assert yourself as the mom. Especially since you are young, you are always going to be looked at a little more harshly. Not fair, but true. My mom had me at 17 and did it alone and always told me about how rude people could be, so she tried really hard to make me be well behaved so that she didn't have to get the attitude from people. And I was a pretty easy-going girl, boys are waaaay harder. I have a 2 yr old son, and my husband is gone a lot, so I am basically a single mom. It's exhausting. And I usually have no clue what I am doing. So don't feel like a bad parent, you are doing your best. All I can say is keep doing what you are doing- ask questions and do research and keep trying, you will figure out what works for you guys. This is a great place to ask for advice, it isn't like asking your mom or aunt or someone. You can choose not to take it and no one will judge you for it. And even if someone gets snotty with you, it's not as bad as hearing that kind of thing from family. Your pediatrician is another great resource. Ask them any and every question you might have, that's what they are there for. Don't listen to your brother, unless he is going to give you rational valid advice, then forget about it.
As far as the no sleeping goes- mine is and always has been a terrible sleeper. I just assumed that people started out their lives knowing how to sleep. It's like breathing right? How hard can it be? Well, pretty hard. I recommend reading some books about getting your baby to sleep. If it was easy and you were the only one struggling with this, there wouldn't be dozens of books on the subject. You are not the only one. I read and had really good luck with The No-Cry Sleep Solution by Elizabeth Pantley. I don't like the idea of crying it out, so it wasnt an option for me either. Don't push a bottle on him, that is something else you will have to break him of to get him to sleep. Always keep to a good schedule, he NEEDS this. And consistency is the key. That is the key to every thing with children, honestly. Every battle you have with your son will come down consistency. If you aren't, you will lose every time. Another book to try for the sleeping issue is Healthy Sleep Habits, Happy Child by Marc Weissbluth or Good Nght, Sleep Tight by Kim West (those have been recommended to me). Keep reading the books until you find something that works for you, his whole behavior might change if he is well rested.
As for the getting into stuff- babyproofing is really the only way to go. He will get into what ever he can, no matter how many times you tell him no. And he will scream when you tell him no. You can spend all your time fighting with him, or babyproof so that you don't have to tell him no except to the big stuff. He will be frustrated and angry if you never let him do anything. I put away everything I didn't want messed up, or that could hurt him, and let him have free run of most of the house. I don't have to listen to myself saying No No No all day or him screaming that way.
You are not doing a terrible job. You care enough to try to fix things right? That is more than a lot of parents. Get on a good schedule, be firm and loving and consistant, and just remember, they don't come with a manual. It takes time to learn how to be a parent.