I'm trying to answer each point in order here...
Experience plays a huge role in counting waves. It's relatively easy to do, but some other factors go into choosing more and less probable counts. There are three simple rules to EW; 1)Wave-2 can not retrace more than 100% of wave-1. 2) Wave-3 is never the shortest wave. and 3) Wave-4 can not retrace into the price territory of wave-1. If you strictly adhere to these rules, it's not so hard. Then there are also a handful of guide lines that make things clearer, though the guide lines are not rules, but more often than not, waves follow the guide lines. Things like Alternation; Says that if wave-2 is a sharp correction, wave-4 will be more sideways and vice versa.
Fibonacci makes the targets a piece of cake as long as you have the right count. For instance, My previous wave-V count was invalidated, but since my targets were hit leading up to the invalidation, the latter waves were counted properly, but something else was amiss. That is when I revise my count and decide where things changed. Some counts/targets can also be correct but take vastly different paths to get there, which is why I have many running counts at any given time.
Intuition should be left out, as difficult as it may be. It is the same as a gut feeling, and while you may be right some, or even most times, it's no different than a guess. EW is a way to gauge probabilities and manage risk by having stops (which I will get into soon). It also tells you what is possible and what is impossible to happen next.
When you have many counts, you begin to see a move coming before it is even expected by your main count. I posted the chart in post #248 because of the underlying technicals and some other things going on. I guess you can say it was intuition, but I felt a change coming that was going to invalidate my count at the time, so I posted the chart. In fact, that is what I use this thread for. Kind of a "thinking out loud" of my thoughts (counts) as the market moves.
I hope I covered everything and answered your question.

thanks for the very detailed explanation ! this makes a lot of sense indeed. Also from what I understand a very important tool in your analysis are oscillators (e.g. EWO and/or MACD), the correct interpretation of which still seems like black magic to me