Yes, you can. WDW admission is valid at DL but not vice versa. Tickets to DL are less expensive, therefore Disney doesn't lose out any money that way. Discounts to DL are pretty easy to come by once you're near the park, we've found coupons attached to large drinks at McDonalds in Anaheim, been offered tickets from local residents at the gate, etc. I wouldn't use up my WDW admission at DL. You can sometimes get into DL for under $30.00 if you do some legwork.
Yes, Walt Disney World ticket media are also valid at Disneyland provided it is a multiday park hopper or PHP with unused major park entries left on it. AP/PAP's are not accepted. You will have to take the ticket to Guest Relations at DL and they will have to call WDW guest relations to confirm that the ticket is still valid because they cannot scan the ticket in California. This is done because WDW admission costs more per day then Disneyland. Plan on spending a little time at the Guest Relations window as this is not a transaction that takes a minute or two.