How often do you communicate with your audience and what would be the best time during the day?

It depends.
Usually, allow one hour or two between posts, so that fans don't feel you are spamming them.
If you are live-covering an event then you would normally do few posts in a short lapse of time.
Just make sure you announce that beforehand.
The same applies to Twitter even though you can post much more stuff in there without being flagged as spammer.
For the posting time, check your analytics tool and it will give you the time interval that gets the most attention froms fans (the most shares, likes and retweets).

This depends on several factors, the basic two are: channel and country.
For Facebook: I would recommend an average of 3 - 5 posts a day (Morning, afternoon, night).
For Twitter: A higher number should be applicable, an average of 7 - 9 posts a day (A post hourly during active hours).
Another factor is countries.
In Egypt for example best times to post to Facebook would be: 11a.m, 2.30pm, 8pm.
For UAE this can completely change to 9am, 12pm, 5pm.