Are there regulations about objects/buildings above (across) taxiways?
Bridges over taxiways are not a common airport feature. The FAA does have standards for wingspan clearance on taxiways, but not heights. Airport information will tell pilots if there are wingspan or height limits on certain taxiways, and ATC will know which aircraft are or are not able to take certain routes.

For example, Denver International Airport has a bridge over one taxiway. This provides 42 feet of tail clearance, which leaves 3.5 feet of clearance for the A320 family (except the A318). These are the typical aircraft that use this taxiway. A 737 classic would have 5.5 feet of clearance but the 737 NG and A318 would only have 1 foot of clearance. Since the 42 foot number is only in the center of the taxiway, and accounting for other conditions, 1 foot of clearance does not leave much margin for error. So for regular operations, the A320 and 737 classic are the largest planes that will pass under the bridge.

The bridge at Gatwick Airport provides 22m of clearance, enough for a 747 (19.4m high) but not an A380 (24m high).

This suggests that about 10% margin is enough clearance for taxiway bridges. The FAA requires that taxiways have 20% margin plus 10 feet to objects. While wingtip clearance has many variables that require larger margins, tail height will not change much.