Hi Anastasia, and welcome
And well done too, it sounds like you're really clued in to your LO which is so important
The newborn phase is tough, please be assured that what you've described is completely normal, I think most of us are here because we didn't find EASY, easy
The colic peaking between 6-8 weeks is actually pretty textbook, really tough, but you should just about be coming out of the worst of that...
Shh pat is really hard work, actually if she's falling asleep by 30mins that's pretty good, some take much longer. At this stage it's really a tool to help teach them how to sleep independently one day, and you can do as much 'work' as you need. In the long run it's better to do it whilst they're in the crib, rather than letting them fall asleep on you - it's very common for a sleeping LO to wake up once they're laid down, unless they're in very deep sleep. But as you say she's so tired, especially as the day goes on, I'd suggest perhaps doing shh pat in the crib (you can start it on you, but lay her down before she actually goes to sleep and continue doing shh pat there) for the first nap, see how it goes, and if she short-naps and doesn't resettle then feel free to hold her or do whatever helps most to get her to sleep a longer time for her second nap - just to break the cycle. I actually used props much more (sling) second time around because of needing to get out with the older one, but she learnt independent sleep just as well when she was ready, I stuck to one nap at home with shh pat every day and that made it easier when I started more consistent sleep training around 4mo. Just saying this in the hope that it will reassure you that you're not too late
Do you have any props that work at all for sleep? I don't think I'd have survived without the sling
Another thing - bear in mind that some LOs don't like the shh, others don't like patting and prefer rubbing or a gentle pressure, etc etc. so feel free to play around with shh pat until you find something she seems to respond to.
The waking at 20mins sets off alarm bells (not major ones, don't worry!) for me as both mine struggled with silent reflux which caused discomfort/pain. Apparently waking at 10/20mins can be related to that, so perhaps something to look into? Or gas? Do you think there's any pain/discomfort? I don't want to worry you unnecessarily so if you don't think so then feel free to ignore that!
My other question is how long is she up at a time? So, from the time she wakes in the morning for the first feed, until the time she falls asleep for her first nap - how long is that? At 2 months I'd expect around 1h to 1h 15mins max, or she may be overtired and so short-nap. Actually mine needed slightly shorter 'A times' at that age.
Oh and another question - is the room really dark? Some LOs find it makes more difference than others, but I'm convinced it's made a big difference to mine, as babies neither would sleep if they could see anything at all - even in the sling I had to cover then up (safely so they could still breathe!) so they couldn't get distracted by other things they could see.
Glad you've found us, hope you find these forums as useful as I have (and still do!), all the best as you begin this amazing, though exhausting, journey