I don't believe there is a better way you can do that problem (5, and the same goes for 6's first step) given your class content.
Problem 4:
First step is OK, but oxymercuriation reaction yields the markovnikov product, and you need the markovnikov. I'd rather go for boron once again.
In regard to the two different Hg reactions, sulphuric acid is just playing a role as a catalyist, and in some cases reaction will work better if you include it, and in some cases it will not. I don't know to what extent adding sulphuric acid is mandatory in this reaction, I'm sorry.
Problem 6:
First step OK.
But you can't perform the hydroboration directly on the haloalkane.
First you need to eliminate the bromine, obtain a double bond, and then get your antimarkovnikov alcohol product.
Problem 7:
First part is OK (although the first two steps can really be just one, heat the starting material with H2O/H2SO4 and you will obtain your third structure)
But that route is not very nice, since in your last step, you cannot selectively oxidize one of the alcohols leaving the other one nonoxidized.
You should find a different path, in which the oxidation step only takes place in one functional group of the molecule (i.e. the other -OH has not been introduced yet)
Hint: Be careful with the second step of the alcohol formation by oxymercuriation reaction, NaBH4 also reduces ketones to alcohols