It sounds like you have gotten some of your questions answered
I realize that everyone has to start somewhere and that you have a mentor and that is wonderful. It is far and away the best way to do it. Please have the vet show you how to handfeed and then watch you do it so he can advise you on the proper technique.
In addition to this, just because you have two birds of opposite sexes and they are mating it does not mean you will necessarily get eggs. So you need to decide if you are going to encourage breeding or discourage it. Light, diet and cage set up is different based on your goal.
If you are not planning to breed then you should keep their daytime light hours to about 12 hours of light and 12 hours of dark and not provide a nestbox. Diet would also be different for breeding or not breeding. If you have done the right research then you should be coming across this information.
Personally, I am happy to chime in but if you truly have a mentor then they should also be helping with this and you should be informing them of what is going on so they know the details. That is what a true mentor would do. Take you through step by step. If that is what you have then take full advantage of it.
Sometimes with vets it is more of an emergency help situation and that is needed as well, just be sure you are clear on how much help you will be getting and is it after hours help or just when the vet is in the office. Babies are 24/7.
Many do discourage people from breeding in general. That is not my intent but while you will never be fully prepared be sure and have all your resources in place, and then some.
One question that has not been asked is do you know the history of the birds and whether or not they are an unrelated pair.
Finally, coparenting is a nice plan but sometimes parents do not feed their chicks. Being prepared and able to feed day 1 babies and knowing whether to take them from the parents or leave them is tricky and this is when the babies are most fragile. Your mentor can should help you with this.
Leaving babies with their parents for as long as possible is the best for them.
I have three pairs of caiques and they are all different and all unique, not one pair has ever consistently cared for a full clutch of babies without intervention. There are hardline people who will tell you that they only way for the parents to learn is to let them do it all on their own and eventually they will figure it out. I am not one of those people who is willing to lose chicks to find out. I always go with what gives the chick the best chance of survival and still have lost chicks and I have lost eggs.
Breeding is not for the faint of heart. Keeping all the babies is also not a viable option. Those babies will grow up and then you will have to worry about them breeding which you will have to prevent because you should absolutely not breed brothers and sisters together. So even if you plan to keep some babies you will need to find homes for the others if not the first time then future times. Eventually the question becomes, where will you put them all.
I have 6 caiques, I know for a fact that I only have room for 8 total. I don't plan on adding more to even get to the 8 so I start lining up homes up to a year in advance. This is what it takes to do it well.
Again, I don't discourage breeding per se, but I definitely don't encourage everyone to breed.
In short, in order to be prepared you need a brooder, a mentor, a way to heat water, a gram scale, extra cages for the babies, thermometer, extra dishes, cages, toys and supplies. You also need handfeeding formula. You will need to disinfect your tools (I boil water to disinfect feeding items and use various chemical disinfectants for brooders and bins. You also need solid information on your species of birds not just breeding in general.
I would start making friends with people who breed green cheekeds. Realistically you also need to figure out what to do with all the babies. Oh and you don't mention color mutations, there is a proper way to breed conures according to their mutations. Sadly, most people do not pay attention to this at all and all the work that went into producing the color variations has been muddled up and lost (that's a totally different topic all together).
Lots of food for thought.