You correctly suspect that “make” is associated with creation. Conversely, “do” will be associated with completion, especially completion of actions and work. For a more in-depth look at the differences, let's start with a readily available resource.
From the Woodward English site, the top-ranked result in a search for “do vs make”:
When do you use DO?
DO is used as follows:
1. DO is
used when talking about work, jobs or tasks. Note,
they do not produce any physical object.
- Have you
done your homework?
- I have guests visiting
tonight so I should start doing the housework
now.
- I wouldn't like to do that job.
2. DO is used when we refer to activities in general
without being specific. In these cases, we normally use words
like thing, something, nothing, anything, everything etc.
- Hurry up! I've got things to do!
- Don't
just stand there – do something!
- Is there
anything I can do to help you?
3. We
sometimes use DO to replace a verb when the meaning is
clear or obvious. This is more common in informal spoken
English:
- Do I need to do my hair? (do = brush or
comb)
- Have you done the dishes yet? (done = washed)
- I'll do the kitchen if you do the lawns (do = clean, do =
mow)
When do you use MAKE?
[1.] Make is for producing,
constructing, creating or building something new.
[2.] It
is also used to indicate the origin of a product or the
materials that are used to make something.
- His
wedding ring is made of gold.
- The house was made of
adobe.
- Wine is made from grapes.
- The watches
were made in Switzerland
[3.] We also use Make for producing an action or reaction:
- Onions make your eyes water.
- You make me happy.
- It’s not my fault. My brother made me do it!
[4. We use make with] certain nouns about plans and
decisions:
- make arrangements
- make a choice
[5.] We use Make with nouns about
speaking and certain sounds:
- make a
comment
- make a noise
- make a speech
[6.] We use Make with Food, Drink and Meals:
- make a cake
- make a cup of tea
- make
dinner
Now that we're on the same page, let's apply this knowledge to your examples:
I made supper.
This fits “make” sense 6 above, which is really just a special case of sense 1. The thing being constructed (so to speak, out of various ingredients) is a meal.
I'm doing my homework now.
This is essentially the first example in sense 1 of “do” above. Homework generally consists of one or more tasks, and is done like a job.
He made it easier.
This one's a little trickier, but it falls under sense 3 of “make” above, which is all about effecting a change in something (or someone) else. In cases like these, the phrase can easily be rewritten without “make” by using some form of “cause (it) to (be)”. For this particular example, you are essentially saying
“He [caused] it [to be] easier”, but that isn't how anyone is likely to say it in everyday parlance.
Note: I've extracted the key distinctions in my block quotes, but be sure to click the link above if you are at all interested in more examples, a helpful chart, and/or a practice test.
Also, please comment if there is some particular aspect of this distinction that is still bothering you.
The difference between college and university is everything or nothing, depending on where you are in the world. There are a number of threads on the matter at EL&U, for example “In college” versus “at college” versus “at university”, “When I was in college…” Do you really mean college? Or university? and University vs college vs academy vs institute vs community college.
In different countries, they may refer to different types of institutions or different levels of education, or may be alternative names for the same type of institution or level of education.
University is reasonably universal in referring to a postsecondary institution which grants academic degrees in a diversity of subjects. College, on the other hand is considerably more diverse in its usage. In the U.S. alone, an institution called a college may be a secondary school, a two-year tertiary institution, a four-year undergraduate institution, a unit within a university (whether academic or physical/architectural), or a university itself— or, the common name for tertiary education in general, or a building or campus.
So, the answer truly depends entirely on context.
Best Answer
For your system, the terms you want to use are:
Explaining why you need to use "make" instead of "brand" is harder than I expected, though. The words "make" and "brand" have the same meaning, we just tend to use one more often than the other when talking about certain types of items. There isn't always a good reason for why people use certain words.
When talking about your favorite brand of clothing, peanut butter, software, shampoo, or pretty much anything other than a car, you generally use "brand". For cars, you almost always use "make".
You would never say, "This is my favorite make of clothing".
"This is my favorite clothing-maker" also sounds a little odd.
For cars, people do sometimes say, "Here is a list of top car brands," but that could just as easily be "Here is a list of top automakers".
If asking or describing the manufacturer of a specific car, though, you definitely want make. As the text you posted points out, it just sounds odd to ask someone, "What brand is your car?" even though they would still understand you and answer the question.