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.