Questions for breastfeeding and pumping mommas!

Abbie
So my baby is 2 weeks. Iv been ebf since the beginning. I want to start pumping but have so many questions. 
Don't necessarily want to pump to freeze, I will do so if my supply allows it. I want to still be breastfeeding the majority of the time but mainly so that dad can help with midnight feelings so I can actually get some sleep. Also so that I can leave the house for an hour or so and not worry about baby going hungry. Also to give my nips abut of a rest because although we've got the latch down they are still recovering. 
Baby is feeding on demand and cluster feeding right now. Any tips or info would be appreciated but I also have a few questions that I would love to be answered. 
1) how to store my milk? Like I said unless I have loads I won't be freezing. I will more than likely be pumping for the same day or the next day so will just refrigerate. Do I still put them in the little bags? Or can I put it in her bottle already and in the fridge? I have a few of the little plastic containers but can you recommend any storage options for me. 
2) I have an ameda pump. What should I buy for it? Like the extra accessories or more of? Do Madela bottles attach to all pumps? 
3) how often do you sterilize your pump parts? 
4) how to heat breastmilk? 
5) how do you keep milk cool when going out? (Another reason I want to pump as I can't breastfeed discretely therefore can't breastfeed in public) but how do I keep it ok when out of the house in this CA heat? - how do I heat it when out? Also can baby drink it cold? 
6) when should I pump? Is it ok to pump only after iv fed her my boob and she's asleep? It's kind of hard to know when cuz she cluster feeds and if she falls asleep she will go 2-3 hours before waking but if she stays awake she could be on and off the boob for 3 hours or longer. 
7) how to keep my supply up? I would like to be able to make enough to freeze too. 
Any other info would be great I literally have no idea what I'm doing lol