There is no set fast that is optimal in one weeks time for achieving what you want. There’s also no easy fast. Water only fasting requires that you supplement properly with electrolytes at least after 48 hours or so. I wouldn’t recommend fasting or attempting a weeklong fast if you are not experienced. You could try experimenting with intermittent fasting, 18:6 or possibly OMAD (one meal per day). If you are consistent, just sticking to 18:6 will improve your mental clarity etc.
In terms of what breaks a fast, it’s typically anything with calories. So, electrolytes and minerals are usually fine. Herbal teas and black coffee may be fine. But if you are adding things to your tea like sugar or milk of any kind, you are not really fasting. I have done different kinds of fasts and up to 8 days with no calories or coffee. I definitely experienced mental clarity and benefits doing that but I wouldn’t start out that way.
OMAD is probably the best to be honest, it’s great. OMAD is my daily routine while I often will do extended fasting, that way there is practically no way you gain weight back. And I think that is a good thing to have, a plan to fall back on basically.