Bit of a latecomer to this thread but just wanted to echo what other posters have said.
My DS (now 12) was a terrible sleeper when little and cried all the time. He had reflux (badly, he was sick after every feed) and nothing we tried worked. It got better when he started weaning which we did at 4 months even though they advised 6 (not sure what the current recommendations are). Heartburn runs in our family and even now he can't eat late as if he lays down too quickly after eating to sleep it is guaranteed he'll be sick in the middle of the night!!
I did use dummies (much to my DM's disgust) but it took a few different types before I found one DS would accept (in the end it was the MAM ones) and he naturally stopped using them when he was less than 18 months so I didn't have to worry about weaning him off them.
But I empathise completely with how isolating and exhausting it is having a baby that cries a lot and doesn't sleep well. I don't think there's always a fix - some babies really are just criers and bad sleepers! The good news is they all outgrow it.
If it gives you any hope, I found things hard going on and off until DS was about 2. Since then he's been an absolute dream. The only challenge I have these days is persuading him to brush his teeth 🤣
I split with DS' dad when DS was 2 and a half. He still sees him twice a week but it isn't always a case of it makes it better. We have had issues with a massive lack of self confidence and an obsession with weight because of his dad's attitude towards him. Its been very difficult because he is smart able and healthy but he hears the bad things and they stick more than the positive things me and my now partner say to him. I have zero control over how his dad parents him when he's there and I have to actively disengage from him constantly belittling my parenting and bombarding me with messages about how I should be being a better mother. It's natural for you to want baby's dad around but very often it causes its own issues.
I'd also second involving child maintenance now. We set up an informal arrangement and I wish I hadn't. It would cause world war 3 if I went to CMS now but I just have to trust that I'm being paid the right amount, there's been issues before with payment dates changing at little notice when finances were tight for me etc and it is more of a tie than if you do it through CMS. If you carry on with an informal arrangement there will be so many discussions over the years whereas doing it formally its all done for you. Kids get more expensive as well once they need formal childcare etc and you may well need payments to be reliable at that stage. Your ex's financial stability is not your concern. That is for him to worry about.
I was on my own for 5 years before I met my now DP and it is beyond tough being a single parent but it's also quite rewarding. You don't have the constant push and pull of differing parenting opinions, if you're having a tough day and don't feel like doing the cleaning/cooking then there's no one to criticise and me and DS were really close. I love DP and he is so good with DS but sometimes I really miss when we were just a team of 2.
Your love for your baby shines through in all your posts. Whatever you choose, dummy or no dummy, classes and groups or staying at home, formula or BF etc etc...your baby will be fine and none of this will matter in a few years time. The decisions that feel monumental and all consuming now and make you second guess yourself will be things you barely remember. I couldn't tell you which of DS' peers used dummies or were formula fed etc. They all seem to be doing OK regardless!