jj74 is correct, there's an error in the mechanism of the first reaction.
For the third reaction, I'm not really sure what you're trying to accomplish by reacting the alkene with water first and then with methanol. A direct reaction with methanol seems much simpler.
The fourth reaction lacks the bromination reagent, but assuming that it's molecular bromine you'll never get a single stereoisomer. There's no chirality in the starting material, so you'll always end up with a racemic mixture. However, I'm not sure if the presence of the hydroxy group really has an influence on the reaction pathway.