OK, these are just my OPINIONS, so don't take them as fact -

1. What is the most reliable, hardest to counter, strongest formation? Does it even exist?
What is your strongest eleven in a formation that is solid? (As in you might have 5 MC's as your strongest players but you couldn't play all 5). For me I have never strayed far from the traditional 4-4-2 and look for players that fit in that formation. I then look for the weakest player in that formation and look to replace him. I personally never try to counter other formations - apart from changing mid game depending on if I am winning or losing. Personally I'd say have faith in your own team and don't worry about others.

2. Does the defensive approach have any big benefits? What about counter-attack forcing and offside traps (never read offside in the live commentary)?
Offsides do exist in the game but the developers said they don't include them on the updates as it would annoy people (this was a reply to a question to the developers last year). I can't say I've ever bothered much to change the approach prior to a match, but often go either more attacking or defensive during games depending on my result. It's impossible to say if it has had any impact on my results but I'd like to think it has - as that is a big part of tactics. If what we do when the game is on is irrelevant then its a shame.

3. Long or short passing?
Why not both? If a team is predictable its easy to beat.

4. How risky is hard tackling? Because even my strong backline gets passed easily.
A few people tried changing from normal to hard tackling a while back to see what the increase in cards were. The result was that it didn't really impact on how much bookings teams got. Personally I find with hard tackling my defence plays better - but that's just personal opinion.

5. Is it recommended to use arrows on all players and overall how should certain players be adjusted (red/blue)?
I've never bothered with the arrows. That isn't to say that they don't work but I like to keep it simple. Keeping it simple stops mistakes from being made long term.

6. How the $^&!# can I make sure my players take 1-on-1 chances?
Nothing you can do about this. Its just the game engine - sometimes they will score, sometimes they wont.