I will almost always wipe it with a towel, but I only clean the grooves if I'm not the last one to hit my approach shot. With the guys I play with, I'm hitting last pretty regularly. That gives me time to clean grooves as part of my pre-shot routine. It also means that once I hit, everyone else is typically walking, so I feel like I need to keep pace.
After the shot only if it’s muddy. Before every shot though I do. Wet the club, wipe it off with my towel. Tee to the grooves if something won’t come out and repeat water/towel. I carry a bottle specifically for it.
Yeah if there's dirt on them. Quick scrub with on of those wire brushed and a wipe with a towel. I have a dirt towel for the clubs and a clean towel for my face and hands.
Yes. I have a brush on my bag and usually more than one towel. I sometimes give them a little water bottle squirt, another reason to bring along a water bottle.