Regulate and control are similar in meaning, but they are not exact synonyms. When referring to government actions, the meaning of regulate is usually
to make regulations for or concerning
(http://www.merriam-webster.com/dictionary/regulate, definition 1b2)
Control is a little more general, and often is used to mean
to exercise restraining or directing influence over
or
to have power over
(http://www.merriam-webster.com/dictionary/control, definitions 2a and 2b)
So the original sentence means something like:
Production, distribution and sale will stay in private hands, but the government will have power over the whole process and will make regulations concerning it.
This is a fun question, because it reveals something about English that I never noticed, even after speaking it for 42 years or so.
Your professor is partially correct, but there's more to it. "At your age" is a set phrase with a negative connotation that almost always means, "...you should/shouldn't be doing the thing I'm about to mention or just mentioned." Another common construction using "at" is "at the age of X," e.g.:
He left home at the age of 16.
("At the tender age of...", indicating youthful innocence, is a common cliche.) "At the age of" feels like formal or written English, whereas "at your age" is casual speech (and maybe a little dated). You can also omit "the age of" and just say, "He left home at 16," wherever it would be unambiguous to do so.
Now, for your first sentence:
When I was a student ______ your age, I tried out for our school volleyball team.
Neither "of" nor "at" sounds remotely natural to me. The best words to put in the blank would be nothing at all ("When I was a student your age..." is perfectly natural English) or "about."
"Boys of your age" and "boys your age" are both acceptable. However, "When I was of your age" is not. I'm having trouble figuring out what the rule is, though. Anyone?
Finally, I've never heard "sweetheart" used as a verb, but it sounds so nice I wonder if you're quoting a famous line.
Best Answer
IMHO, you are right.
When something is under control, it means that we are in the situation of monitoring it. However, when a thing is in control, we can command and direct it.
From Collins Dictionary:
The Collins English Dictionary stresses on the harmfulness of what is under control.
Also from dictionary.com:
in control: able to direct a situation, person, or activity.
under control: (of a danger or emergency) such that people are able to deal with it successfully.