First of all instant coffee is evil stuff!! If you're going to drink coffee drink the real thing. Instant coffee has very little coffee in it at all.
As for the hot water - I only drink warm water now and it has helped me enormously. Warm water with lemon first thing in the morning is one of the best things you can do for your liver. and yes, prior to a meal (at least half and hour before though) is also good. Cold water is actually quite a shock to the body - warm water is much more easily absorbed and you'll find your body responds so much better to it. Coffee does take a while for the liver to process. I'd honestly wait till your liver was a bit healthier before going back on coffee. Whilst it's unwell, anything like that is best holding off on in order for it to heal. But a coffee every few days is fine I'd guess???