How hard is it to ban and pick heroes without letting an opposite team know what strategy you're actually going for? Are there any set patterns that tell you very clearly what's going on?

Most new strategies which are made do not involve the need of banning some 4 same type of heroes, but when there are, it is very easy to understand where this game is going. There are of course strategies which involve outsmarting the enemy by banning some type of heroes to make them think you will do a certain thing. Many of these can backfire, but are very interesting if you think about it.

How often is counter banning and counter picking used and how effective is it?

Can always be effective, especially if you nail it.

                                          Puppey thinking how to nail it

How big is the importance of the so-called initiator heroes (heroes that initiate teamfights)?

The importance of every key hero is big o.O, if you initiate to meat (basically initiate with yourself as a sacrifice), can't be called "important", but in 2v2, 3v3 fights and in picking off heroes they are important.

What are the usual reasons for banning a hero?

Too noob to play it, hate it, imbalanced, MiseRy loves the cock and so on. But mostly banning for strategic reasons.