This should be posted in the "Help and Support using Construct" section (along with your .cap file, maybe) .
I'm not the best person to ask but you could make a variable called "cheeseeaten" and have it's value be "0" at the start of the layout. When the character's sprite touches the cheese you could change the value to "1".
You could then make a condition starting with the system object that compares the global variable "cheeseeaten" to see if it is equal to "1". If it is equal to one then you could use the "create object" option (system) to make another piece of cheese at the same coordinates as the original (don't forget to reset "cheeseeaten" to 0 afterwards).
I'm not sure what your problem is with adding points when you get the cheese, though. You said that you already have a scoring system?
Just make a global variable called "cheese" and have it's initial value be zero. Make a "trigger once while true" condition and make it so that when the character sprite touches the cheese sprite it increases the value of "cheese" by one.