Will android market work (update app) after I install a new mod in my phone
CyanogenMod is not permitted to redistribute Google's proprietary apps packaged with the ROM, but they make them available separately. As long as you download and flash the latest Google Apps package from your recovery system, you can continue to use the Market as you normally would.

The newest versions of CM are (according to the wiki, anyway) designed to actually backup your Google Apps during the install and then re-install them for you, but I've had mixed results with this so I typically just install them manually after installing CM.