CDP directly into amp?

You can, but it needs to be a CD player with a built-in volume control (otherwise you need to use an outboard volume control, passive preamp, or active preamp). It will sound best if the built-in volume control is a good one (preferably analog) and the output of the CDP is a good match for the input sensitivity of your amp.

This topic has come up quite often. Search the archives for CD players with volume control and you should find a bunch of info on this topic (and many CD player recommendations too).

Yes you can. Ideally your CD player will have a quality volume control, high output, and low out put impedance. Your interconnect should be short and have low capacitance. The McCormack amps are particularly good choice due to their rather high (for solid state) input impedance and IMHO it's punchy extended sonic signature. Choose a McCormack that is on the sensitive side. The cons include a varying impedance depending upon volume setting and the chance of diminished dynamics.

Of course if you have a CD player that you like and wish to keep, an alternative would be to consider an amplifier with an attenuator on board - or an integrated amp. But the advantage of an amp with an attenuator is that it will typically sound better than a comparable integrated amp (at least that is what I have observed in my own listening tests) The only problem is that sometimes amps with attenuators lack remote control functionality.

Otherwise both Phild and Unsound have offered the exact same advice I would throw your way in terms of cables, and considerations for variable out CD players. And yes McCormack would be a great amp to consider if you plan to use a CDP with a variable output stage. There are other good choices as well but if you like the sound of a McCormack, it has the right electrical characteristics to work in such a configuration.