Can an attorney represent a client against a previous client, without notification to the previous client?

The answer from Justin Cave adequately addresses this point.

If No, will case be thrown out upon being made known to the Court or must case be appealed on that fact alone? What types of damages are those?

None of the above. If this happens the former client may ask the Court to disqualify the conflicted attorney from representing his current client in the case. If this isn't done, any consequences in the case are waived.

The attorney could also be disciplined by state attorney ethics officials. The punishment could range from a private reprimand to disbarment, depending upon the severity of the violation and the attorney's history of previous ethics violations.

Can an attorney represent a client against a previous client, without notification to the previous client?

The answer from Justin Cave adequately addresses this point.

If No, will case be thrown out upon being made known to the Court or must case be appealed on that fact alone? What types of damages are those?

None of the above. If this happens, the former client may ask the Court to disqualify the conflicted attorney from representing his current client in the case. If the former client doesn't do this, any consequences in the case are waived. It is not a basis for an appeal if no motion for disqualification is filed, it is not a basis for throwing out the case, and it is not the basis for a claim for money damages.

The attorney could also be disciplined by state attorney ethics officials, if someone files a complaint with them. The punishment could range from a private reprimand to disbarment, depending upon the severity of the violation and the attorney's history of previous ethics violations.