Q) Does CUSIP in CDA correspond to NCUSIP in CRSP, and does TICKER in CDA correspond to TICKER in CRSP?
A) Your best choice is to use the CUSIP in Thomson and the NCUSIP in CRSP -- both are historic.
For the non-matching cases using the CUSIP, then use the ticker. Tickers are less reliable because they change over time and are reused. Moreover, Thomson and CRSP are not required to record the same ticker for the same stock. It is usually the case, but not always. With tickers, there is more margin for error.