well thats just your ear, you need to develop it more so that when you here a note you know what it is. Unfortunately there are no "tricks" for this that I know of. Since it is in your head you are the only one who can figure it out.

Try humming it that might help. But ultimately it is your ear which is gonna do the work there.

As for which instrument to record first it shouldn't matter to much if you can hear every part in your head. I would try and figure out which one is laying down the base of the song and record that first. the one that is in the back mostly, holding everything together, that will make it easier to record the other instruments over it which might be dropping in and out.

But yeah one of the best things you can do as a musician is train your ear, it should happen over time anyway but actively training it can speed up the process.