How do know if a salt is more soluble in acid like HCl than in water? For example why is PbF and AgSO4 more soluble in acid than in water?

More soluble salt....

Both PbF2 and Ag2SO4 are sparingly soluble in water.

You wouldn't use HCl for PbF2 or for Ag2SO4 since PbCl2 and AgCl are insoluble salts themselves. A better acid would be nitric acid, HNO3.

PbF2(s) <==> Pb + 2F- ............... Ksp = 3.3x10^-8

The addition of H+ will cause a reaction with F- to make undissociated HF, and lower the F- concentration, shifting the equilibrium to the right, causing more PbF2 to dissolve.

Ag2SO4 <==> 2Ag+ + SO4^2- ........... Ksp = 1.2x10^-5

The addition of H+ will form HSO4^-, reduce [SO4^2-] and shift equilibrium to the right, causing more Ag2SO4 to dissolve.

You need to look at the anion in the salt. If the anion is a conjugate base of a strong acid then it will have no affect on solubility in an acid. If the anion is the conjugate base of a weak acid then that base will react with some of the acid and cause a shift in the equilibrium.

F- is the conjugate of the weak acid HF

SO42- is the conjugate of the weak acid HSO4- (note that it is not the conjugate of the strong acid H2SO4 as only the first "H" is strong in sulfuric acid)

One way to look at it using PbF. If you have 100grams of water, there can "fit" a certain number of F- ions. Now if you have some acid as part of that 100g, it will consume some of the F- ions you put in there. But you can still fit the same number of F- ions, so some more PbF will dissolve.