These are all terrible things to deal with on a daily basis, But there are solutions to these problems.
Humidifiers help with static shock, dry air, allergies, and make your home feel more comfortable in the dry winter. It makes a big difference believe me. For allergies or asthma, breathing problems you can try electronic air cleaners, hepa filters, electrostatic air filters or uv lamps. these will usually get 99% of the dust particles and pollen out of the air and do a good job. The uv lamp and electronic air cleaners do a good job of getting rid of odors also.