You can change the location of your .mpr file (move to another directory) and try to open project via recent projects menu on start page, it will throw an error message and give you the option to remove project from recent project list
I know it is not the best solution but works - havent found any menu settings for this issue
No you can't right now except through using the method described by Karol.
However I've requested this feature last year and it should be added in the future. The current info in MXDN is:
Caller: Jaap Pulleman
Type: Feature request
Name: Recente projecten kunnen opschonen (ability to clean up recent projects)
Expected: 3.0 alpha