Well, you have a lot of questions at one fell swoop here, and they kind of paint a picture. It seems that you've gotten into a "holding pattern" and don't know how to keep up, both with your child and with your boyfriend. What happened to your relationship with him? You don't go from having sex, getting pregnant, and then 18 months of nothing without something being wrong between you two, unless one of you decides they are no longer in love.
Children's developmental phases move fast and you need to learn to keep up. Read about child development so that you know what you're dealing with and what's probably coming up.
I don't know how it is that you still have a boyfriend after 18 months of no sex. Turning your man on isn't what you need. You need to connect with him on a personal level and talk to him about it. Ask him to be honest with you, listen to him and then decide what you are going to do. It sounds like he is now a friend and the father of your child. If marriage is not on the horizon, you need to go find a job to be ready for the day that he doesn't support you.
Work with your daughter on her speech. Most of the time with this age, the tantrums are because they don't know how to express themselves any better than this. When she cries for milk or water, say to her "You want some milk? Milk! Yes, this is mmmilk! Here's some milk!" "Wah-wah - you want some wah-wah? Can you say wah-wah?" When she gets frustrated because she can't do something, teach her the words "help me" by saying 'ep me. "Honey, you can tell mommy 'ep me, 'ep me!" You have to do all this over and over.
One of my sons had a pretty severe speech deficit. Nothing he said was intelligible and he didn't try for the most part because people couldn't understand him. When he was 24 months old, I had his speech evaluated and then started speech therapy. What I have told you above is exactly what my son's speech therapist worked with him on and what I worked with him on at home. These are not "baby words" I'm explaining to you. These are ways for a toddler to be able to try to make words. Always acknowledge verbal tries with a smile. When you can't understand the words but have an idea of what she wants, like, say, if she wants to climb up on the couch, teach the 'ep me. And then help her if she tries. She needs to know that she gets somewhere with trying to talk to you, instead of just screaming.
You need a play pen, pack-n-play, or something to actually put her in when she has a tantrum. That way she won't hurt herself. Everytime she starts, try to redirect her so that maybe she'll forget. Redirection is better than "No" because she can't think through "No" right now. She's too little. But if redirection doesn't work and she has a full blown tantrum or starts hitting you, then put her in the play pen, tell her "No hitting Mommy" and walk away. Don't be in her view at all during these meltdowns. When you can tell a difference in the tone of her cry, go back in to her and pick her up and love on her. At the point that her cry is different, then she is missing you and forgot about what her tantrum was about. If she hits or kicks you again, you didn't wait long enough and you put her right back in the play pen and walk away.
Don't lecture her. Keep it short and simple. "No hitting Mommy" and that is that. You have to be 100% consistent.
Don't take her places before a nap. Don't take her out when she is hungry. Excursions out of the house should be when she is well rested and full. If she starts a tantrum in the store, leave your cart and take her straight to the car and strap her into her carseat. Stand outside of the car and pretend to read a book. Pretend that you do not care one bit that she is crying. Ignore her. After a bit, open the door and say to her "Are you done?" and watch her reaction. If she looks like she wants a hug, take her out of the carseat and hug her. If she's over the tantrum, tell her that you are going back in the store, but if she cries again, she will go back in the carseat.
You have to do all of this over and over and over. You don't tell an 18 month old, or 2 year old, or 3 year old, etc etc something once or twice and expect them to understand and "obey". It is a process of much learning, and only works if YOU as the adult are consistent.
You have said you want to get some childcare for her (I don't blame you - you need a break) but if she has these tantrums and hits other adults, they'll probably throw her out of the program. Work on YOUR END of handling things better with her before sending her somewhere where she won't be successful. You don't want to get a great center and then lose it.
Really take stock of things in your life right now and be resolved to understand what is happening and move forward instead of just letting things "happen". You need to gain some foresight on a lot different fronts right now.