There's an old riddle that goes, Q: "How do you eat an elephant?" A: "One bite at a time."
You've got a lot going on and these obstacles seem insurmountable. So you don't try to solve everything at once - you prioritize and you make a series of smalls steps which will eventually lead you to your goal.
You are emotionally overwhelmed - you have lost your mother, you have a new baby, you are alone without the baby's father, you have an infant, you are hormonal, you have moved to a new area, and you are living with an entirely new family situation (new personalities, new dynamics, new pressures). While your father and stepmother are giving you a roof over your head and some financial assistance, you're also getting some pressures. So of course it's hard to know which way to turn.
Start with you and the baby. Thank your father and stepmother for their help and tell them how much it means to you. Then yes, apply for whatever assistance is available and for which you qualify. That's why it's there. Don't let anyone lecture you about what you should've done differently or how you should be completely competent to handle everything on your own. Do not let other people's judgments, whether they are in the form of Mamapedia answers or the looks/comments you get in your town, derail you. Just because they say it doesn't mean they are right! It's easy to criticize, and it's a lot harder to walk in another person's shoes. So, contact WIC and apply for state assistance - get good advice from someone at WIC or whatever other agency you contact. Get food stamps, medical care for you and the baby, get a good pediatrician if you don't have one already, and whatever months income you're eligible for. That's what taxes pay for - when you go back to work, your taxes will contribute to repaying that. Don't worry about it now. It's a safety net designed to help people short term when they need it. If you worked before you got pregnant, your tax money contributed to this anyway. No matter what, helping someone like you get back on her feet is a good investment of my tax money, that's what I think.
As about other forms of support services. You are still adjusting to being a mom, which is exhausting and confusing. You can learn more about infant care and get some strategies for making things a little easier - every new phase a baby goes through (sleeping through the night, getting teeth, self-soothing, colic, you name it) is a new stressor for the mom. Getting into some counseling, a parenting group, an infant first aid class, a breastfeeding support group, and grief counseling (since you are mourning the loss of your mother as well as your former town and relationship) are all good first steps. You may have some depression, either post partum or related to losing you mother, and that can be paralyzing and overwhelming.
That way, you will take care of yourself - that has to happen before you can look into meeting someone else's needs in the workplace. You're no good to a company or a boss if you're exhausted and stressed.
It may be worth getting some advice about pursuing the baby's father for support, but that's not first on the list. People can be tracked through social security numbers and their wages can be garnished, so don't write that off just because you don't know where he is right this second. Sometimes agencies that help people like you also have courses in things like household budgeting, checkbook/financial management, and other helpful adult skills that you may not have gotten because your mother died before her time.
Next, try not to be overwhelmed by pressure to put your baby in day care. Yes, infants as young as 6 weeks can go, but you have to find a job that pays you more than the day care. So you can go to your state department of employment or workforce development (different states use different names) and see what's available for job training (if you need it) or in the field for which you are trained. Find out if your certification is good in your state (since you moved from another state).
Don't worry about the advice to sue a prospective employer who turned you down because you were pregnant. It's wrong for them to turn you away but it's way too much energy for you! You need to move forward!
Once you get some state assistance, have a talk with your father (and maybe your stepmother) about ways you can help out while you work on a plan to get a job and get your own place. If you have a little income, you won't need to live off their generosity as much. You can do your own grocery shopping or you can pay a small amount of rent, whatever works out. Don't over-commit right now - just make some small steps. You can show your appreciation perhaps by doing some housework or sharing the cooking duties. You mentioned in your other question that they have a 9 year old daughter. Perhaps you can trade off some child care, watching your half-sister sometimes, and having them watch your baby while you get a break, go to a class or counseling session, or go to the job placement bureau. Maybe if they see you taking some steps, your stepmother will back off on her pressure.
Meantime, you can use the programs you attend as a way of networking about lower cost child care, perhaps subsidized housing, etc. You may need to get your name on some waiting lists but the sooner you do this, the sooner you will get to the top of the list. Don't be discouraged by long waits. Just get on lists, and keep plugging away in other areas - maybe you'll get a good job with a good child care option, maybe you'll get into a training or certification program, maybe there are more possibilities that we can't even think of right now.
The main thing is to come up with a 2 year plan, with a few steps for each month, but NOT trying to solve it all right now.
But take care of yourself so you can be a better parent to your daughter. On airplanes, the safety presentation tells adults to put the oxygen mask on themselves first, and then attend to their child. So don't sacrifice yourself so much because you are worried about being a perfect mom who is there all the time for your daughter. Don't think about what you "can't do" (I can't get a job until my child is in school, I can't find an apartment, I can't get child support) - think about what you "can do". Every step is important and worthy of recognition.
Good luck!