First off balloons dont very gently ascend or descend, as a fixed wing pilot you need to understand never fly directly above a balloon, our rate of ascent is multiple times yours 1000fpm not a problem, easy and is the normal reaction from a pilot in trouble above a certain altitude (few dozen/hundred feet), so dont try to out climb us, we will all be in trouble. go around.
we go the speed of the wind, while birds do fly into my picture window of my house, because it sometimes looks like it isnt there and they want to land in my living room. they dont often fly into brick buildings just for fun nor will they fly into a massive balloon that is going really slow compared to them.
you dont launch unless the winds are favorable, ideally under 10 mph on the ground and that speed or less during the flight as you often fly in the morning and upper winds drop so while you can get up to 20+knots that is still slow compared to a bird.
If the bird cant see the 2/3 story building in front of them even the largest bird is not going to cause a serious problem. the are likely to bounce off the fabric not go through it, if they go through the hole wont be that big, as answered it is not pressurized like a helium latex balloon, the whole thing is leaking air (very tiny amounts but non-zero) unless brand new and even then...its not like a tv show I saw where a small 1 inch hole near the throat needed macgyver to climb up and fix it. that is just silly. by the through you are legal to fly with small holes at above the equator the rules change but it is per manufacturer. you can technically fly with a big rip in the side, being rip stop nylon it doesnt increase unless the fabric is in bad shape which means you didnt pass inspection which means you are not flying so that is not a problem.
I had heard of an RC plane intentionally fly into a balloon because they were tired of balloons flying over their field on the weekends, not realizing this is a federal offense, the biggest problem for the pilot was a plane falling down through the throat with the prop spinning and not getting injured from that. Same would be for a bird if it were even remotely possible to break through, I cant think of a bird that is that fast, narrow with that sharp of a pointed beak that could even attempt such a thing and would have to do it intentionally. I dont think a hummingbird has the mass to get through. anyway if that were to happen then the next concern is the bird trying to get out through the throat. the hole in the balloon would not be too much of a concern, could still land the balloon, etc just couldnt fly again until repaired.
never heard of a bird strike, would have to be a pretty dumb bird, and likely would just bounce off, if it were to penetrate likely would be only the beak to the face, then the bird would wiggle out, that hole would not be a concern other than found during pre-flight and not get to fly or found during annual inspection and require a repair.
re-reading your question it is very uncommon for mid air collisions even during events like fiesta, but that depends on your definition, because of how close quarters have gotten, four balloons per square at fiesta or more, you rub against others all the time and rub on the way out, sometimes basket to envelope, but usually that is a pilot mistake. You are most likely to see a balloon to balloon collision at fiesta in the air specifically but not at other rallies as others only have one wave/row of launches not three like fiesta. Once aloft mid air is very very very rare even at fiesta as you cant steer your way into one.
Your assumptions in general about balloons seem to be off. Rate of climb, number of mid air collisions at rallies, etc...
Balloons are both quiet and noisy, the silence to loud would keep birds away if any were nearby. The inflation fan is noisy and would keep them at a distance, the inflation is noisy would keep that at a distance, and it is a flying house that is usually bigger than the trees that they can see and not hit but instead land on. It is quite hot as you get close they could no doubt feel that, etc.
Birds are not a concern.
Other balloons are not a concern. Any more than other planes are an airport to a fixed wing pilot. Everyone follows the rules/procedures there are no issues.