I have a firearm and went through the process, I'll try to answer what I can.
Under the "Apply for a permit" tab, one of the requirements are, "Name, address, and telephone number of the seller." Does this mean I already have to know which store I'm going to buy the firearm from?
Usually when people are getting a permit, it's because they're registering a firearm, that's why that is on there. Honestly don't waste your time getting a permit if you're not getting a rifle at the same time. The permit only lasts a year so no point waiting your time.
One of the forms to fill out is "License to Carry a Concealed Firearm Application." If I'm getting a rifle, I'm assuming I don't need to fill this one out?
You do not need to fill this out. Hawaii is a state where carry permits are ONLY granted by the chief of police and you need cause to carry (job, extreme fear for your life, etc.). Don't bother because no citizen has been given a permit to carry.
It looks like they only need one form of ID, so my driver's license should suffice?
Yes
So after I get my permit after the 14 days I can bring that permit to a store and buy my rifle, then within 5 days bring it back to the police department and get it registered. It looks like the permit expires every year and but can't find any info on the registration, so it looks like there's not expiration?
Go to the store you want to buy the firearm at and talk to them. Honestly they know the process best and will able able to help you. I highly suggest you take the class so you can know proper safety, handling and care. Playing CoD doesn't qualify you to own/operate a firearm and even if you think you know what you're doing, you don't. Take the damn class, more information or a refresher won't hurt you.
The process I took was this:
Be sure you understand the firearms laws, there are laws with firearms that you probably don't even realize are laws. Be especially careful with firearm laws as they can often times end up with felonies.