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

Anyway keep up the great work !!
Let me explain this a little. Indicators such as MACD and EWO are momentum indicators and RSI is a strength indicator (it's in the name

)
As the price is rising through wave 1, the market is hesitant about a rise, so selling pressure is still present and early buying pressure is beginning to show itself. This creates a small bump in the underlying indicators.
Then wave-2 starts and people who think it's only a correction sell hard. This is why wave-2's are usually much deeper corrections. This also makes the indicators return to where they came for the most part.
Enter wave-3.. This is where many people begin to see the buying pressure, and in fear of missing the train they panic buy "before it's too late". The causes a large spike in the indicators and is resposible for the massive power of 3rd waves.
Wave-4 begins, and with a reluctance to sell, the market meanders sideways for a while. Sometimes twice as long (in time) as the wave-2. The stability makes some less experienced traders sell, and the lack of buying (after all, we must be at the top, right?) allows the indicators to return to a more neutral state, EWO returns to the zero line which by this point, is way down there.
Once we break up from the 4th wave, those who sold are essentially tricked into buying back. By this point, asks are pulled in search of higher selling points. The price moves very easily with much less force, and the volumes are much lower compared to the 3rd wave. This keeps the indicators from making that big spike we saw in the 3rd wave. That combined with the lower starting point and weaker momentum creates the divergence that signals a topping situation (higher price high with lower indicator high). Then when the smart money has squoze all they can from this run, they hammer the price lower in the larger degree wave-II and it all cycles like that... In both directions, over and over and over...