To add more fields to the calendar display use the display attribute. To change the color use a field in the color attribute. To change color conditionally then add a compute to the color field in the model.

<calendar string="Itineraries" date_start="start" date_stop="stop" date_delay="duration" all_day="allday" display="[name] - [extra_field_1] - [extra_field_2]" color="colour_partner_id"  mode="month"> 
    <field name="name"/>
    <field name="extra_field_1"/>
    <field name="extra_field_2"/>
    <field name="color_partner_id"/>
</calendar>

To add a clickable button to the event you will need to extend the web_calendar module's javascript in web_calendar.js.

I would think the event_data_transform function would be the right place to add a button.