Firstly, in both cases, F is more EN than I, meaning that it has the ability to attract electrons (or electron density) towards itself in a covalent bond.
BUT, it is also important to remember that atomic radii is coming into play. Atomic radius tends to increase as one proceeds down any group of the periodic table. This makes sense since atoms with more electrons have larger radii. So let's analyze.
HF vs HI:
Since I is farther from H, than F is from H, and since F is more electronegative, H can more easily dissociate from I. the H's are being held onto with less strength by I (Additionally, in terms of acid strength, the more stable an acids conjugate base, the stronger the acid. I- is more stable than F- because it's electrons have more space, and are dispersed better.
I3CCO2H vs F3CCO2H:
Since F is more electronegative than I, it is pulling electron density (termed inductive forces) away from the Oxygens (which are resonance stabilized btw). So instead of focusing on the F's and I's, let's focus on the oxygens now. in F3CCO2H, the oxygens have less electron density than in I3CCO2H, and now the H's are being held onto with less strength by oxygen in F3CCO2H, and have an easier time leaving.