You should be as honest as possible with your attorney so that he or she can represent you in the best possible fashion.  Anything you tell your attorney is priveleged and confidential, as long as you are not discussing committing a crime or some tyoe of fraudulent act.  Your attorney is obligated to keep all discussions with you private.

Yes, definitely. The more your attorney knows, the better he or she can defend you (including being prepared if the prior crime comes up). Owing to attorney-client privilege, you can safely share this information in confidence with your attorney, with one caveat: if somehow the information is related to a present or future threat to public safety or a future crime you are planning to commit, the lawyer may be obligated to disclose it. As long as its safely "over and done," the attorney-client privelege will protect you.

The attorney client privilege is a doctrine that exists to promote communication between lawyers and their client.  Everything you tell your lawyer in connection with you seeking legal advise is considered confidential.  Your lawyer will not tell anyone what you say - i.e. it goes to the grave with the lawyer.  This way, clients feel free to provide their lawyer with as much information about the case as possible to help them with a defense.  You should tell your lawyer about everything.  Even if the charge was dismissed, you want him to know about it.  As long as you are not seeking advice to engage in a crime or commit fraud, everything you say when you seek legal advice in confidential.