Congratulations! Getting 4 foot tall coffee trees from seed is quite an accomplishment.  Coffee plants can become infested with white fly which sounds like what you have, mealy bugs which are white, but don't fly - they are flattened, aphids or scale. You could send close-up pictures for a more definitive identification.   To treat your plant use a soapy mixture for about 2 weeks.  You can also use insecticidal soap which is gentle and organic.  Safer is one brand and others should be available at your local garden center.  This article has good information on growing coffee, All you need to know about growing coffee trees in your home.

The brown on the ends of the leaves looks like sunburn to me.  Most of the leaves look fine.  Coffee plants don't like direct sun.  An east window would probably be a good sun exposure for them.  They also really like high humidity, but don't like soggy conditions.

White flying bugs are probably White Flies.  This article gives you pictures and possible treatment.  You should see adults, eggs and nymphs on the undersides of the leaves - but they're tiny.  White flies can be a big problem in houseplants and greenhouses.  Gnats are dark.  They can be a nuisance, and the larvae eat fungus living in the soil and roots of the plants.   Fungus Gnats gives you pictures and more information.  You might see black-headed larvae in your potting soil.