1)
Why did Elisha command Gechazi to run to greet her?
1.
Malbim: Since she comes not at the proper time, surely there is a problem, due to her, her husband or her son.
2)
Did she say Shalom before Gechazi spoke?
1.
Rashi: No. The verse is abbreviated. It omits that first Gechazi asked her, like Elisha commanded.