How safe is it to go over a speed bump at a decent speed say 15 mph on a road bike? I feel some rattle near my rear derailer does this damage the bike at all? I'm running a 25 tire on my caad Optimo 4.
Speed bumps are very variable.
Some I can take flat out (more than 20mph, but that's the speed limit there) briefly standing, or seated at about 12.5mph (converted from 20km/h as I think in metric) .
Others, when I get to the station on the same commute, are intended to slow cars to 5--10 mph and are best avoided. It's possible to dodge them but if for some reason you can't, stand up and take them dead slow.
The speed limit is a good guide to how fast you can take them, if you're willing to stand up on a road bike, even though that's meant for cars. Slower if you can't.
Rumble strips designed to provide a tactile warning of a reducing speed limit are worse. Some are nothing, but others require a very firm grip on the bars and standing at any speed. You can't always tell until you hit them.
It is safe if you prepare even a bit, have your hands on the handlebar and lift yourself a bit from the saddle and absorb the bump with your knees. Full weight on the saddle is not likely to damage the bike (except maybe the tires if you have very low pressure) or send you flying, but can be very uncomfortable.
"Rattle near rear derailleur" can be either the lower run of the chain rattling or something that is actually loose. The chain can damage the finish on the chainstay. If it worries you, there are protective tapes and wraps that you can use.
Road bikes are surprisingly sturdy. Even the very light ones.
Some very light (or badly built) wheels can be a bit weak but usually you are more likely to sprain your wrists than damage the bike. Unless you are heavy (>90kg) or riding with luggage.
It’s still a good idea to get your ass off the saddle and soften the impact as much as possible. If you are in gears which put very little tension on the chain (smallest rear sprocket and small chainring is the worst combination) you are more likely to get chain slap against the chainstay or the chain could even fall off the chainring.
Also make sure your tyres are properly inflated or you can get a pinch flat (or rim damage in the worst case).
The rattle is likely just your derailleur bouncing and the chain hitting the chainstay. In general I'd deem it harmless. Most road bikes and hybrid bikes do not have clutched derailleur. For road/gravel cycling Shimano just recently introduced their GRX line designed for gravel which includes clutched derailleurs (a feature that has been in mountain bikes for a long time).
A clutched derailleur keeps the chain under tensions which lessens the frequency of chain slap (the chain hitting the chainstay) and the chain coming loose. Road bikes tend to not have this feature as it's not necessary. It would prevent some noise but it's generally unneeded complexity and cost.
I'd make sure your chainstay has at least a clear film protector on it. On an alloy frame such as yours it's more of a aesthetics standpoint (alloy won't rust) on a steel bike paint chips can lead to rust.
I ride speed humps (long speed bumps) at 25+mph. The trick is technique. I pull up on the begining and push down like I'm pumping on a pump track. On a short speed bump as pictured I'd likely slow down a bit and pull up just as I hit the bump and absord the real wheel going over with my legs.
If your tires have sufficient air pinch flats shouldn't be an issue. Tubeless can also solve that (no tube to pinch with the rim).
I know roadies that bunny hop up and down curbs all the time with no issue. It won't damage your drivetrain.
I don't believe the very small speed bump the picture shows would do any damage.
I ride at 15 mph over far larger speed bumps. I have 28mm tires. I have never had a pinch flat when riding over speed bumps. Pinch flat is your largest concern -- if riding over uneven road will do something damaging to your bike, it's gonna be a pinch flat and it's less than half an hour and maybe $1 patch to fix it, faster if you're experienced.
The only damage I ever have was the kickstand bolts self-loosening (this obviously doesn't affect you unless you have a kickstand). I suspect this was caused by riding on bumpy roads at great speeds. Then I used thread glue on the bolts. Self-loosening problem solved, but the kickstand has become somewhat wobbly because I no longer tighten the glued-in bolts, and road bumps have probably removed a lot of aluminum from the kickstand to frame attachment area. Some day when the kickstand becomes too wobbly, I will remove the glued-in bolts, cut an old punctured inner tube, make a piece of rubber between the frame and kickstand with two bolt holes, and attach it with bolts glued with thread glue. I suspect the rubber will eliminate the material removal problem, meaning the kickstand no longer would become wobbly.
I would say, it also depends on the speed bump's shape and size. If it is flat and curved, it's probably not much of an impact but if it is high enough, you might get some micro-airtime that can unsettle your bike, I've also seen plastic ones with an edge on private property that are good for a pinch flat or possibly even rim damage.
So, in case of doubt, slow down if safely possible, especially in traffic or group rides - point it out for the ones behind but focus on making it over the obstacle yourself. Approach it straight, stop pedaling and get out of the saddle to absorb the bump. The latter mainly for your comfort but also to avoid a crash when you get knocked off the bars because you were tucked in.
I'm surprised that nobody suggested bunny-hopping but I'd not advise it because you can get over it in most cases without and there's a risk of the back wheel hitting the bump, unsettling your bike and causing a crash, that's more an advanced technique for serious obstacles like potholes or rocks.
A combination of low pressure tire, heavy rider, fast speed, high bump and zero care about all this happening may result in a pinch flat. I was getting them before I learned to pay attention. It is possible to feel a much harder "hit" when the rim takes over the impact, no longer the tire. I never had crashes or other kinds of damage but likely also might happen.
This can be avoided by standing on the pedals, limiting speed and crossing near the edge of the road where these bars are often lower (or even do not span the complete width).