Do I need to tune all lines e.g. the drums? Or does this only affect the bass line because it has the lowest notes (&the lowest note defines the chord)?
Tuning has nothing to do with chord progressions. If your instrument is tuned properly, it can play any chord. All instruments in an ensemble-- including the bass-- should be tuned to the same base frequency, usually A = 440 Hz (or a multiple thereof).
Some instruments, such as cymbals and many drums, are not capable of being tuned, of course, so don't worry about those.
Some instruments are pitched instruments but cannot be tuned. An example would be the xylophone. For those, you may actually wish to tune the rest of the ensemble to that instrument instead of 440 Hz.
For the most part, composers do not worry about tuning at all. Instrumentalists worry about it. Composers just assume that all instruments are tuned properly, unless they are a very avant garde composer doing something very unusual, e.g. if you want the second trumpet to tune a quarter step off so that your trumpet section can collectively play a 24-note scale.
Should the other lines start with the root key of that chord or can it use any of the chord's notes and still be harmonic? I know that you are not 100% limited to the chords notes e.g. if you want to create tension. But does it sound harmonic?
Generally speaking, different lines can play any note in the current harmony, and often play notes that are not in the harmony, e.g. passing notes. There are no hard and fast rules for this. Doubling of the root is definitely not required. If you're asking what notes "sound harmonic" (sound pleasing), there are hundreds or thousands of books written on that sort of thing.