shiro and suru in this sentence?

I saw this question in an N3 study video, and didn't understand the answer given. I forgot which video it was, unfortunately.

お父さんは厳しい人で、自分のことは自分でしろと言われてきた

I'm not sure if I remember this sentence correctly, but it shouldn't be too different from the original. There were four answers, but I only remember two of them. する and しろ, with the later being the correct answer. Why is する wrong in this sentence? I'm also a little confused about the usage of しよう and しろ. I think the former is a suggestion, while the latter is more forceful, is it?

Thanks in advance!

Yes, “しろ” is an imperative (an order/command, telling someone to do something), and “する” is the original “to do” dictionary form/ru-form.

Actually this sentence would be easier to understand if you add/change a bit:
お父さんは厳しい人で、（私は）自分のことは自分でしろと言われてきた
So the sentence is saying:
- My father is a strict person, and I have been told (by him) to do things on my own.
Therefore it is referring to the part that the speaker was “told to do” by that strict father, thus the order/command form.

しよう is rather a suggestion, invitation, or showing willingness as in:
テストが近いので、もっと勉強しようと思う。(As the exam is approaching, I think I would study more.)
新しいレストランができたから、一緒に行こう！(There is a new restaurant, so let’s go together!)

…whileしろ is really someone senior (like a teacher, a parent, a boss, etc.) “telling someone to do something.”

「お父さんは厳しい人で、自分のことは自分でしろと言われてきた
Why is する wrong in this sentence?」

The problem with using する here relates to 「お父さんは厳しい人」

Let's look at the two options you're considering:
「自分のことは自分でしろ」
「自分のことは自分でする」
The first one is "Do your part by yourself." It's a command, and so it sounds strict (especially with the use of しろ instead of して).

But the second is a more general statement of "People [should] do their part by themselves." While some people might say that's strict, many people would say that's common sense and responsibility, so
「自分のことは自分でする」 doesn't really mark the father as a "strict person."

Because of that, 　I don't think I'd go so far as to say
「お父さんは厳しい人で、自分のことは自分でしろと言われてきた」
is 100 percent "wrong," but it's a little unnatural, because it's saying that the idea that people should take care of their responsibilities is 「厳しい」.

On the other hand,
「お父さんは厳しい人で、自分のことは自分でしろと言われてきた」
because of its use of the very forceful しろ, and the fact that it's a command, does sound strict, especially when paired with 「言われてき」, which implies a one-sided form of communication that took place over a long period of time.

Again, I don't think it's so much a case of する being "wrong" and しろ being "correct" so much as する feels unnatural and しろ feels natural. Because language isn't an exact science, a lot of tests will ask you to pick the "best" answer (not the one-and-only grammatically possible one), and between する and しろ here, しろ is definitely the best one.

(same poster as above)

「 I'm also a little confused about the usage of しよう and しろ. I think the former is a suggestion, while the latter is more forceful, is it?」

Yes, in general しよう is a suggestion, and しろ is a command. So 「それをしよう」 would be "Let's do that," and 「それをしろ」 would be "Do that."

However, just like in "let's" in English, しよう is sometimes used as a very soft command, especially when speaking to small children. Like if a kid says they want to put their toys away later, and a parent wants them to do it now, they might say 「今しよう」. Grammatically it's a suggestion, but really it's being used like a command.

This also ties into the topic of
「お父さんは厳しい人で、自分のことは自分でしろと言われてきた」
versus
「お父さんは厳しい人で、自分のことは自分ですると言われてきた」

The combination of 「お父さん」 and 「自分でしろと言われてきた」 again marks the dad as a strict person, because even when speaking to his child, his words are framed as 「しろ」, when a parent who was being kinder/more delicate would have used 「しよう」.