Methyl Tert-Butyl Ether/ Ether Cleavage

So I have been working on converting methyl Tert-butyl ether(MTBE) to t-butanol, but it seems I have had no success. To be honest this was really my first go at organic synthesis and I am sure I made plenty of mistakes.

The final product does not seem to react with HCl to form T-butyl chloride and it is not a solid at room temp.

The quick version of what I attempted to do is, React MTBE with HCl to get t-butyl chloride, Hydrolyze the T-butly chloride and get T-butanol, distill T-butanol from reaction mixture(water/acetone)

From this I have a couple of questions:

When cleaving tertiary ethers with HCl should the mixture be allowed to reflux or is leaving the mixture to react at room temp for >12 hours sufficient?

Can t-butyl chloride hydrolyze when being washed to remove residual HCl?

I've also read that ether's can be cleaved with dilute sulfuric acid, but I was unable to find a procedure for such a reaction, If anyone knows a reference to such a procedure please share.

Any thoughts or ideas on how to refine this procedure or come up with a new one altogether.