To achieve a crust on the outside while keeping the interior of the steak cooked to your liking, you need to have two different temperatures set on your grill. In order to get those nice grill marks, you need to heat your grill to high heat to essentially sear the steaks. To determine the heat is hot enough, you should be able to hold your hand about an inch over the grill grate for 1 second before it feels too hot and you must pull it away.
Seasoning a grill has no relationship to seasoning the steak or eggplant you're grilling. In the latter case, you season to add flavor to the raw food item. But when you season a cast iron grill, you're not adding flavor. It actually refers to the process of coating the grill grate with oil, then heating it, to render it rustproof and create a virtually nonstick surface. Depending on the type of grill you own, you may only need to season the grill the first time you use it and occasionally after that. And with a Weber brand grill, you may not need to season it at all.
Clean the exterior of the grill. Soapy water is the safest cleaning solution for most gas grills. Just make a cleaning solution with water and a squirt or two of mild dishwashing soap. Wipe the exterior of the grill with the soapy water, use a rag dipped in clean water to remove the soap residue, and then dry the exterior of the grill thoroughly.