If an event is on the calendar for 10pm Monday to 2am Tuesday, the calendar agenda displays this as two events. One from 10pm - Midnight, the other from Midnight - 2am on the next day.

Since the event doesn't start on midnight, I would really like to see the event listed starting on Monday at 10pm and the end time shown as 2am, and on the Tuesday agenda listing, it would not be present at all. Or, to put it another way...only events that start on that a day or events that are marked as all day events for multiple days, should be listed in the agenda on that day.

As far as I can see, the present ways to move accross views are mainly the 'day slider' and the menu (and a tap on the month name from year view). The 'day slider' can even be hidden wich makes the menu the only way to proceed.

Could there be some gestures (swipe, single/double tap) , accessible in all views, to navigate faster?

As single finger swipes are already used, I propose to use two fingers swipe to do so.
Sweeping left/ right would navigate accross day/week/month and year view in that order.
Sweeping up (or down) from week view would go to the agenda view.
A good example of such possibilities is 'aCalendar' app.

Arrow buttons could be an alternative but I don't see much free space for that.

Double tap on limited zone displaying month name, week number, day number or year number is possible. This replaces the need of a button by a zone that already displays a useful information and is simultaneously a button.

A limited zone from where to start the sweep is another possibility. Example: leftmost/topmost centimeter of the screen as when you pull down the android notification panel from the launcher.

Thank you

Please add a widget which can be placed as one of the four main apps at the bottom of the home main screen.

Click on the widget will open the "new task" window with active text form.

So it's like: click on the widget > type text for the task > press save which will return us to the home screen where we have started.

Less clicks much more effective for quick adding.

Please take a look at application called TickTick from which I came to you. They have this beautiful feature and it was the only reason which was stopping me of moving to BC2.

The idea is that I am able to add the new task by 3 seconds: unlock phone > open widget (which is always on the home screen (4 main apps bar) > type text (leaving default settings for new task) > press save (which returns to the home screen where I have started).

Also please add two different options for this button: either to add the Task or Event, so people don't need to waste time on choosing the type every time they want to add new task or event. I will add these two buttons into main apps bar (four main apps at the bottom of the home screen)

Rythm of the life sometimes does not allow me to select the needed home screen to find a widget, then press "+" then choose the task or event, then saving will take me to the app itself which I don't want and to lock the phone I need to close BC to save battery, so it means long press on home button and closing app there. Imagine how many seconds for one task add.

If you are adding 50 task per day, 5 seconds on adding a new task which we can save are crucial.