Hey Joy,
I’m sorry to hear about these issues. For starters, yes, you do need to keep The Events Calendar active to have Events Calendar Pro active.
As for the performance concerns, can you clarify how many events you have on your site, to the best of your ability? Do you have thousands per month, for example? Hundreds per month?
One quick thing that might help is to go to Events → Settings → Display in your wp-admin and check the “Enable month view cache” option:

This should speed up the month view page, at least—though I’m sorry to admit that there aren’t many other things you can do from a simple in-plugin options panel or something to make significant impacts on performance.
— George