Goldfish and Live Plants

Anacharis supposedly does well in cooler temps anyways, low 70's are ideal.

And no, ich needs a fish host. Plants can carry other "pests", such as snails or algae spores, but not diseases.

The best ich method is to raise the temp a few degrees and treat with salt (aquarium salt, or regular table salt works just as well)...I don't remember exact doses however.
 
It is possible to bring in fish pathogens on plants, but unlikely. In addition, in order to get sick there needs to be more than just the pathogen present, there also needs to be a stressor. If the fish is not stressed it won't get sick (at least not when it comes to ick and other common fish diseases).

In my experience a truly complete and balanced diet can lead to goldfish not bothering plants because they don't need anything from them. I have a ton of plants in my 150 goldfish tank and they don't bother any of them. I feed New Life Spectrum exclusively.

Anacharis is fine in room temperature. Good lighting helps, anacharis will root and make a good addition to your tank. Some basic easy fertilizers can help as well.
 
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