What is this fungus -- can my houseplant be saved?

Hard to tell from the photo, but it may be powdery mildew.

http://www.veggiegardener.com/diseases/powdery-mildew/

http://organicgardening.about.com/od/diseases/p/PowderyMildew.htm

Those are bugs, not mildew (sorry, I can’t remember the name). Spray them with insecticidal soap which you can get at any garden shop.

@snowberry some kind of scale insect. You can physically remove all the ones you can see, but some kind of spray is a good idea. You might want to make sure they’re not on the roots, as well. I don’t know if they will go in the soil, but I had some on an orchid once and they did go down in the bark and get on the roots.

Following @ccrow‘s lead, I found this.

Check out aspidiotus destructor, a white scale that is a common pest for banana and coconut trees. It is classified as an armored scale and doesn’t oozee the sticky honeydew that the common hard reddish-brown scale I see on my house plants does.

http://www.extento.hawaii.edu/kbase/crop/Type/a_destru.htm

To give you perspective, go to Google Images and type in scale insects. Then do a different serch for mealy bug. I think you have mealy bugs. I am not sure if they are a type of scale but it looks like it. Both can be removed the same way. Very interesting.

@snowberry: I am learning more about this than I probably want to.

Mealy bugs are “insects in the family Pseudococcidae, unarmored scale insects found in moist, warm climates.”