Does exist any horn formula that is equisatisfiable to the clause that is disjunction of two literals? Does also exist equivalent?
The answer is no: this is not possible. I assume a horn formula is a CNF formula with at most one positive literal (=nonnegated variable) in each clause. Now, for the sake of contradiction, suppose we have a horn formula $\phi$ that is equisatisfiable to $p\vee q$. Since $\phi$ is a horn formula, each clause in it contains a negative literal OR there is a clause consisting of only one (positive) variable. If the latter is the case, that positive variable must be a helper variable, since if it were p, it would mean that p must be necessarily true for satisfaction, which is not the case in "$p\vee q$" (same argument for q). So in this case, we derive an equisatisfiable formula by replacing that variable with true. In this new formula, we have one less clause that contains only a positive variable. We repeat this process until this is no longer the case, until we have a formula that has a negative literal in each clause. But such a formula is satisfiable by setting every variable to false. However, that's not the case in $p\vee q$, hence the contradiction.