Do all heating and air conditioner units have air filters?

Yes they should, however the filter is just to keep debris out of coils and blower section. Keep in mind though the total static pressure for most units is a 0.50 iwgh. This budget is figured with a 0.10 iwgh for the return, another 0.10 iwgh for the supply, 0.20 for coil, and leaving the last 0.10 iwgh for the filter. not saying that removing the filter doesn't actually increase the cfm delivered because it does, however soon a unfiltered coil will become impacted and require an acidic or foaming agent be sprayed in-between coil Finn's in order to return the airflow back to acceptable level for heat transfer.