Alabama and South Carolina are both members of the Drivers License Compact (DLC) and Non-Resident Violator Compact (NRVC). This first compact requires that the Florida courts inform the Alabama DPS of your daughter's out of state speeding offense if she is convicted of it. The NRVC requires AL to suspend her license if she fails to pay the ticket or otherwise take care of the citation.
Section 32-6-14 of the Code of Alabama states that the Director of Public Safety shall also file all accident reports and abstracts of court records of convictions received by him under the laws of this state and in connection therewith maintain convenient records or make suitable notations in order that an individual record of each licensee showing the convictions of such licensee and the traffic accidents in which he has been involved shall be readily ascertainable and available for the consideration of the Director of Public Safety upon any application for renewal of license and at other suitable times.
Since under the DLC South Carolina will inform the AL Department of Public Safety about the speeding offense and conviction, if your daughter pleas guilty and pays the fine, it would appear that it would then be placed on her Alabama driving record.
You or your daughter will need to check with the Alabama Department of Public Safety (DPS) to find out if points will be assessed. If points are assigned for the SC speeding ticket to your daughter’s driving record, it should be only the 2 points listed on the AL driver license points schedule for "speeding in excess of posted limits."
As for your 2nd question, I believe the officer was trying to be helpful and inform you that the ticket may be able to be reduced if your daughter attends court. She may be able to reduce the ticket or see if traffic school is available to her by simply calling the clerk of the court, the number of the court is usually listed on a traffic ticket.
It would be a personal choice if she wanted to come to court or just pay the ticket and fine as it is. The SC court may be able to advise her if through traffic school or other ways she can reduce the ticket down to a non-moving violation that would not be reported to AL and thus not placed on her driving record.