C needs to be checked only during a cache miss as then only there will be a main memory reference and we have to decide whether to cache that particular page or not.
All others are not always required. If we are not caching a page, then there is no need to do virtual address to physical address translation while looking in cache.
Also, a dirty page can be cached. Dirty bit in a page means, the page is modified and must be written back to secondary memory during replacement. This has nothing to do with the page being cached or not.
http://6004.mit.edu/Fall13/tutprobs/vm.html
