I'm assuming that constitutional matters at a federal level are decided by a panel of judges. Is it then possible for such decision to be hung like what can happen with juries? Are judges allowed to abstain from voting or is it as simple as being put to a vote and there always being an odd number of votes?
Constitutional matters can be, and often are, decided by a single judge in a garden-variety trial court. It's just that the judge's decisions may be reviewed and possibly overturned by a higher court, one of which is the supreme court. Furthermore, district courts are bound by precedent. If a case turns on a new statute, however, the trial judge can indeed find that new statute unconstitutional without a higher court first having done so.
If a panel of judges is evenly divided on whether to overturn a lower court's ruling, the lower court's ruling stands, but no precedent is set.
The supreme court often has an even number of justices hearing a case, whether because of a vacancy or because a justice has recused him or herself.