Depends on the type of decoder installed. Older DCC decoders will not let you operate a DCC loco with DC power pack, but the more recent decoders that have a dual-mode will allow you to run it like a standard DC loco, minus any DCC-specific features of course.
Yes, as M-R-L stated, most decoders allow for running on straight DCC. Some folks have commented that the decoder equipped locos require a higher starting voltage and lose some of the low-end of the speed range, but I have not noticed this at all. I have run locos with Lenz, Digitrax, and "whatever Bachmann uses" on DC with zero problems. As far as vice-versa... In most cases you CAN run a non-DCC-equipped loco on a DCC layout. (some DCC systems don't support this, and others like Digitrax allow you to disable this feature) I personally don't recommend it though. First, a by-product of the trickery involved to get the DC loco to go causes a high-pitched whine from said locomotive. While this doesn't harm the loco per se, it does also seem to cause the motor to run hotter. (which I supposed could eventually harm it) So you would want to keep a watchful eye on any DC loco to make sure it doesn't get too warm. So, just keep those things in mind.
Usually If the decoder has analog/DC conversion then yes. I think most decodes these days have that ability but it needs to be turned on.
Ever since about late 2006, decoders have been dual mode, and certainly all sound decoders in new models since then. The earlier Soundtraxx DSD100-LC models were not meant for DC operation, strictly DCC. So, don't ever put one of those on your DC layout! And, as stated above by Doug A., you can run DC (non-decodered, but DCC-ready) locomotives on some DCC systems that were designed to allow you to run them that way. I think the address 00 is for that on Digitrax, at least it works that way on my Super Emprie Builder's DB150. However, because of the high frequency of pulses emitted in DCC systems, the motor gets excited in a pulsed way, and that contributes to a harmonic jittery effect in the DC motor which results in groaning and whining....most off-putting for the huge majority of us, and we soon abandon all such silly notions. Note that you can get engines off the shelf with a simple DCC decoder, no sound, or you can buy two and three function simple decoders from TCS, NCE, and Digitrax, as examples, for just a few dollars..say $12.
