To answer your questions...
The SCGOP will support Graham with whatever resources are necessary. No challenger will receive ANY support.
South Carolina’s open primaries will allow Democrats to crossover and vote for Graham against anyone more conservative than him. During the last election cycle, his Democratic challenger in the general election was actually more the conservative candidate. It was a weird case of many Republicans voting for the Democrat, and Democrats voting for the Republican.
That said, I am sure Governor Haley’s endorsement of Lindsay Graham is on it’s way.
But he shows really well in polls too, doesn’t he?
I just can’t see what GOP voters like about him. I’m in the Northeast, where GOPe/RINO types are to the left of a lot of Democrats in other parts of the country, but SC isn’t that overtaken by folks from up here, is it?