When to open the bar?

I would open the bar at cocktail hour. If the bridal party arrives early I would have maybe small cans or bottles of drinks in the bridal suite for refreshments but I wouldn’t be opening the bar before the ceremony if you aren’t offering an open bar.

I wouldn't worry about covering a round before the ceremony. I would rather know that there aren't random people drinking on your tab by keeping it closed until cocktail hour. If the groomsmen really want drinks before the ceremony they can buy them. Will the bar turn into a cash bar after the $5,000 limit is reached? If so the hosted bar should last you well into the evening. I would consider closing the bar an hour before your exit or official end of the party anyway, people don't need to be drinking until the last minute.

I wouldn't open the bar until after the ceremony for cocktail hour. If the groomsmen want to pregame before the ceremony, I say FH should just bring a bottle for a quick round beforehand.

I would open the bar during cocktail hour but see if you can buy some beer in advance or a bottle of scotch/whiskey for the guys to share while getting ready before the ceremony.

Don't open the bar before ceremony starts

No, open the bar after the ceremony. If the boys want to drink before maybe they can bring flasks, but they shouldn’t be dipping into the wedding supply before it’s even starting.

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Yes, the bar will turn into a cash bar after the limit is reached. The wedding we just went to (with an overlap in friends, slightly larger wedding but not by much, similar priced drinks) went through their $5,000 before dinner. It's a bummer but it is what it is. At least in our area, people seemed to be appreciative of the covering as much as they did and just paid for their drinks after.