Let $G$ be a reductive algebraic group over a complete non-archimedean field $k$. We know that maximal compacts are exactly the same as maximal parahorics when the Iwahori is open compact subgroup of $G$.

My question is exactly when is the Iwahori open compact subgroup? Does it hold for any reductive group or do we need simply connected or some simplicity assumption?

Another question is, could it be that maximal compacts are same as maximal parahorics even when the Iwahori is not open compact?