Yes, by installing a Humidistat.  A Humidstat will reduce the humidity without lowering the temperature in your home or business by reheating the conditioned air.   A Humidistat is installed beneath the thermostat.

Your unit may need to be serviced.  It could be low on Freon, could have dirty coils, or the moisture trap is not properly installed or it is clogged.

Replaceable filter - Change once a month.

Electrostatic filter - Clean once a month.

An air conditioning and heating unit should be fully serviced twice a year:  once at the beginning of summer and once at the beginning of winter in order to keep your system efficient at the beginning of each season.

If you have a problem with dust, an electrostatic filter should be installed in the unit and in each intake in your home or business.  Electrostatic filters are 97% efficient in reducing dust, pollen, and all allergens from your home or business.

You may have an older air conditioning unit with a lower SEER rating than your neighbor.  In order to fix this problem, you need to replace the compressor or purchase a new energy efficient unit.

No.  This problem is caused by low Freon.  The cause could be a result of a Freon leak.  The system should be checked for leaks and serviced immediately.

Make sure your fan is set to auto at the thermostat.  If it is set to auto, then the unit needs to have a full service check to include Freon leaks and a pressure check.  Always make sure that the service technician leaves you with a measurement of the pressures on the high pressure side and lower pressure side of your unit.

HEPA stands for High Efficiency Particulate Air.  It means a filter which is capable of capturing 99.97% of particles as small as .3 microns (including bacteria, fungal and other opportunistic microbiologicals).