Yes Got all the same issues as first poster.
This calendar is perfect for my needs so trying to tweak it as much as possible to correct the glitches i get (with this wordpress theme)
FYI The 2 solutions i made to fix as best as possible.
To correct the header issue, i hid the H1 tag in css on the events-gridview (calendar) and events-list (events list) body styles.
.events-gridview h1 {display:none;}
.events-list h1 {display:none;}
Then i edited the gridview.php and list.php file and inserted a new div H2 and styled to suit.
The date-picker solution, the best i could do was make sure each month has an event added so the date picker wouldnt screw up as mentioned in first post.
Hopefully a fix might come soon, but im looking at updating to the pro version as i really like this calendar. Be nice if these issues i get are fine in the pro version tho.