For the Start screen - it opens on the monitor you last did something in "metro" on. For example, if you opened the Charms bar (Win+C or hot corner), and open "Settings," Start will now open on that monitor. You can always force the Start screen to open on your monitor of choice by opening the Charms bar on that monitor and clicking on "Start" or by using the lower left hot corner. However, there's no way (to my knowledge) of doing this with the Windows key alone.

For the taskbar issue, you can change that. Right-click on the taskbar, choose "Properties." Under "Show taskbar buttons on:" select another option. I personally prefer "Main taskbar and taskbar where window is open." But to each his own.

Good luck!

Full disclosure: I am a Microsoft employee.