You can't get a divorce without serving your spouse with the papers and giving her a chance to respond. You can ask the court for permission to serve her by mail at her last known address or by publication, but you have to show that you have exhausted all reasonable efforts to locate her, so start calling friends and family and try to track her down. (If you have the means, hiring a private investigator may be the easiest way.) You should consult with an attorney before you file anything--if it is not done properly, the court will not approve it.
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(1) Yes. (2) Yes.
(1) Service can be done by getting a court order allowing it to be done by mail or publication. Court permission will be given if you first send the process server to the last known address; the process server then will give you an affidavit of non-service. That's usually enough to get a court order allowing service by mail or publication.
(2) You can do it all yourself. You can also do brain surgery on yourself. But the procedures are complicated for both There are 1000 ways to mess it up the rules about legal service of the pleadings, let alone all the other procedural rules.
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