It sounds like you are feeling really overwhelmed...I know the 24-hour needs of a newborn were a shock to me with my first babe, and the feeling that it was always me, all the time, was very, very difficult. This is a brief period, though - my experience was that by 3 or 4 weeks, we had found a rhythm and I felt much more confident. I think the best advice I received about breastfeeding with my first baby was to be absolutely committed to nursing for at least 6 weeks - and by 6 weeks, we wouldn't have done it any other way. But those first weeks were hard, and I know how discouraging and awful nipple pain can be.
The first thing I wonder is what kind of cues you are looking for, sorry if you already know all of this. With a newborn, almost anything is a cue to feed - smacking lips, stirring around, trying to gnaw a fist, waking up. So feeding 'on demand' doesn't mean you need to wait for a cry of hunger; that's a "late sign" of hunger.
Some babies are sleepier than others and need more encouragement to nurse, and I would err on the side of encouraging the baby to nurse if you are engorged or if she has gone more than a few hours without feeding. The usual advice is one longer period of sleep a day, 4-5 hours, is okay in the early weeks.
With the latch (which is probably causing your soreness), I'm sure the LC or an LLL leader who could see what is going on will be most helpful. In the meantime, tickle her lip with your nipple, try your best to wait for her to open as wide as a yawn (try opening your own mouth saying OOOOPEN) and bring her onto your breast chin first, so that your nipple goes over her top lip and into her mouth. If you are literally using your fingers to stuff your nipple/areola into her mouth, that definitely will tear up your nipples, I know from experience.
WRT sleep, my savior has been side-lying nursing, although I know that can take some time to master when you're struggling with latch. Take your sleep where you can get it, whenever the baby is sleeping or whenever you can nurse and lean back and doze. There's nothing more important to do now than to nurse and rest...you'll figure the rest out in time
I hope this is helpful, and sorry you are struggling. If you can get to an LLL meeting for some in-person support, I *really* recommend it.