Seawater is highly resistive to radio waves at the frequencies we usually use them. (see page 7, section Sea Water.) However, at lower frequencies, 10-30 kHz, it is entirely possible. Unfortunately, this frequency allocation chart shows that the entire 10-30 kHz range is occupied. You'd be interfering with other signals, if you're using the same systems. However, you could set things up in your world so that the 10-30 kHz range is completely empty, at which point you can put radio communications from your city in it.
Your other option, since you're not that far underwater, is to build a big antenna extending above the surface, which you could then assign any frequency to since air conducts radio transmissions.
The alternative, which you can use for many of these sections, is a tunnel leading out that takes you to the surface.
Transport around your city is not a problem - since you're pressurising the whole area, you can just use regular methods of transport.
To get in and out of your city, your setup of airlocks and submersibles is sufficient, but you might want to consider big submersibles for that many people. The alternative, as I alluded to, is to use your communications tunnel to move people as well.
This answer is going to get very boring very quickly if I just keep saying "use the tunnel". However, you could do, just run a big cable down it. The alternative, which is slightly more interesting, is to build an osmotic power plant or salinity gradient power plant, which uses osmosis between and fresh water source and a saline water source to create power. Assuming you also have a desalination plant set up for water, you have both required water types.
Run a pair of tubes up to the surface and stick big pumps on both of them. One of them should pull air out of the underwater dome and one should put air from outside back into it. You could also add some filters if you want really clean air - this might also work as a health centre where people with weak immune systems could come to because you've cleaned the air. Just make sure you decontaminate every visitor.
You need transport for this, basically. The simple solution is to take bags of waste out on every submersible trip and bring in supplies. You could also have some fun by installing a flexible tube leading to the surface and putting some targets around on the surface... trash bag shooting becomes your new sport. Shoot them with air pressure.
For waste water, do what every country does with their waste water already: recycle it. Clean it out, filter it, sanitize it, and put it back into the fresh water system. (If this disgusts you, don't worry - you're drinking the water that someone flushed down the toilet a month or two ago.) You can dump the remaining solid waste into the sea. Again, if you protest violently against this, countries already do it and have done for a very long time.
See also eharper256's comment below this post explaining some alternatives.