Adding Widgets removes current sidebar

You can NOT.
Widgets override whatever is handcoded in your sidebar.php.
Use the appropriate widgets for Cats, Links, Archives etc.

So how can I get the Events Calendar to appear with the other menus… am guessing this is not possible?

Read it again!

[moderated]

I gave you the exact answer above:
Use the appropriate widgets for Cats, Links, Archives etc.

yeah fine whatever mate, if your sick of constantly typing the same answer out, then try not saying it in CAPITALS or with EXCLAMATION MARKS, people may then find you helpful and not some constanly moaning git