To determine whether an attorney is licensed to practice in a specific jurisdiction, you need to look up that attorney in the bar that applies to that jurisdiction.
Some attorneys do not allow their information to be posted on the online lookup, in that case you would have to call the bar to confirm that s/he is licensed.
I assumed you meant more than "case" in the legal sense above. For instance, if you want a Patent, you would need someone licensed to the Pat Bar.
Cases they have worked on:
You can use Google Scholar and select Case Law / the Jurisdiction you are concerned with and search for their name exactly (I would also limit the time frame.) The attorneys for each side are listed at the top. Some of the large cases have multiple pages of attorneys with their name on the case.
Alternatively, if you have a subscription service to WestLaw Next, Bloomberg Law, or LexisNexis you can lookup the attorney and see case information as well, as well as court documents they have submitted in various cases - this allows you to get a glimpse of their writing style. Alternatively, you can visit your local law school's law library and, if they have public access, use the public terminals (at least my law school has these.).