Is it possible that strong acids like H2SO4 behave as weaker ones like CH3COOH when the concentration is really high and vice versa for weak acid? And same question for bases. By this I am generally referring to pH values. Why do conc. acid react more than dilute ones. The degree of ionization of conc. acids are lower than dilute acids, so they were supposed to react less. Or where am I wrong?
A strong acid will always have strong characteristics. What makes an acid strong or weak is the minimum pH required to make it's acid hydrogen (the hydrogen that gets ionized in the acidification of the solution) ionized. The stronger the acid the lower the minimum pH, thus making it possible to make a more acid solution (hence the name strong). Same things for bases, but swap the acid hydrogen by the basic OH.
It is not right that diluted acids ionize less. It ionizes by the same amount (acid's kpa) but the solvent makes the average ionization smaller.
For this reason weak acids make tamponing solutions. When they get near their minimum pH they start acting like a base, deionizing the solution as it gets more hydrogen ions, holding the pH.