I have a commercial appliance that is rated for 230 volt single phase.
All I have available is 208 volt single phase.

Will the unit work on 208V or do I have a problem?

There should be no problem. Esp if the unit is resistance heat.

230 volt heaters will not get as hot as intended when supplied by 208 volts, performance usually not noticeable.

Even motors will operate fine.

If the unit is refrigeration,there is a bit of concern.

Check with the manufacturer of the unit, so as to insure no damage will be done, and performance of the unit will be acceptable.

Can I put 3 number of air con with 1 horse power in my house that has only single phase power supply

Many ACs are rated to run at a minimum of 190 volts before they will have a problem. You should use larger wires to supply the unit when the voltage is lower because the amperage will be higher. You need to check the documents from the manufacturer, but it should be okay. DrTom4444