Is it important for people with congestive heart failure to avoid fats and refined sugar and carbs?

Yes and no: It's important for everybody, including people with chf, to avoid bad fats (animal fats, trans-fats), refined sugar, and simple carbs. A balanced diet includes mono and poly-unsaturated fats, complex carbs and starches and protein, all in moderation. Folks with CHF should avoid salt which promotes fluid retention and htn, and should aim for normal body weight.