In practice there are only two ways to do handle communication: Light trough optical fiber for short and long distance and light in general for short distance communication. Optical fiber can deliver vast amount of data, but in order to work optical computers/circuits would be needed.
Offices, shops etc.
Offices, shops etc. would work same way as private houses would.
Factories would mainly work but they might be much less efficient than today.
Cars would be like described in Non-Electric Car
Trains are working even today with diesel engine. Electronic parts would be needed to replace with other technologies like in the non-electric car has been done.
Especially for subway trains it would be important to develop more efficient exhaust filters.
After modifications also ships would work, but navigation without a radio, a satellite navigations system, a radar, a sonar or a compass would be difficult. A compass is not using electricity but it is using magnetism anyway. Can a solar flare hurt a compass?
Airplanes navigation would be even more difficult than ships.
Main question here is would an airplane fly? Probably, but they would be less efficient, comfortable and safe.