Colostrum collecting

I’m about to start hand expressing (I’m 37+4) and storing colostrum for once baby is here. I’ve been doing some reading, but I want to know what actually works and is simple.

I was going to order the 1ml syringes from Amazon and freeze them once full.

Is it okay to combine the morning and afternoon expresses into the same syringe once both have been cooled in the fridge and then freeze?

Do I need to write the date on the syringes or could I do an overall date on the ziplock bag? (Ex. Sept 13-23)

I’m having a scheduled c section, could I take the syringes to the hospital to use that first couple of hours right after surgery? Would they store them and/or have a way to warm it?