Yes, it's a complicated business, but you'll get through it if you just take things one step at a time. There are lots of people here willing to help with whatever crosses your mind, so just ask.
when I fingers crossed get residency in three years.
Don't build your hopes on getting residency in three years, because it's not going to happen. You can start the application process in three years, and after that,
it will take as long as it takes. If you look at old threads, you'll see that you can't rely on INZ estimated times, because INZ never know themselves how things will go. Already with the new parent scheme, we've seen some people be processed extremely fast, and others sitting waiting with no apparent progress. You've got your plan to get the parent/grandparent visa, and just about the time you can apply for sponsored Residence, you will ALSO be able to apply for a second parent/grandparent visa, so you can keep going to see the family.
Am I able to put the EOI in early so I am not sat twiddling my thumbs after the 3 year period is up?
No, you can't submit your application early. The reason is that the sponsor (your daughter, in your case) having been in NZ as a resident for a minimum of three years is one of the qualifications. If someone looks at your application and sees that your daughter arrived in NZ 2 1/2 years previously, they would be automatically obliged to refuse it.
Medical. It has to be no more than three months old at the time the EOI is lodged - that is, when you send it to INZ, and they accept it into their system (after which it will go into the managed queue until eventually, it is its turn to be allocated to a CO). Normally, the time that passes while an application is with INZ doesn't count to make a medical (or police check, which also has a life) out of date. It is theoretically possible that INZ could ask for these things to be done again, but in practice it's extremely rare.
Passport. Yes, once it's been seen, it can come back to you. When you send in your application, specifically ask for it to be returned as soon as possible, then there's no misunderstanding.