Congrats on your baby.
These first weeks are tough and the cluster feeds are hard work.
Baby does it to help your body understand their demand. As hard as it is, it's part of process of establishing Breastfeeding. It does pass though I promise.
Dad can help you with this by bringing you food and water, by looking after EVERYTHING else in the house and doing nappies. He can also take baby for a cuddle in the early morning if you need more sleep. Also, if dad gives a bottle, you should be expressing the missed feed so your body knows it was needed. It can end up doubling your work load.
On the expressing, at this point you don't want to do too much unless you have to. Your milk works on supply and demand. If you pump too much, your body thinks baby needs more and will make too much.
A Haakaa style pump is great at this stage for relieving engorgement and catching let down. It doesn't over stimulate and is easy to use. You can have it on while baby feeds so it's no more work for you.
I combi fed one baby and EBF the other. Both were introduced bottles the same way. First baby swapped between easily, second baby totally refused. Tbh I think bottle acceptance for breastfed babies is totally down to them.
But, we got some formula starter kit bottles. For the first few weeks we offered an oz a day from one of these. Just to see if they'd take it. Baby one was fine, baby 2 freaked her shit.
If baby refuses a bottle, DONT PANIC. It's ok. Cluster feeding doesn't last forever. Around 4 months they will settle and be feeding less abs likely a bit more predictable. By 6 months you can introduce a cup with weaning. My LG refused bottles, but would take milk from a cup when she was a bit older.
You got this mama.