In

1. I want to say/suggest that a better question to ask is why do you think this class is required for your degree

I would suggest to use a colon to introduce the new question with a question mark because it uses direct address:

I want to say/suggest that a better question to ask is: why do you think this class is required for your degree?

For:

2. Why do you think this class is important for your degree would be a better question to ask students.

I think it's better to introduce quotation marks:

"Why do you think this class is important for your degree?" would be a better question to ask students.

Whereas in:

3. I would suggest that a better question to ask would be why we think this class is important for our degree.

It's more of a general statement so it's fine to exclude the question mark.

In

1. I want to say/suggest that a better question to ask is why do you think this class is required for your degree

I would suggest to use a colon to introduce the new question with a question mark because it uses direct address:

I want to say/suggest that a better question to ask is: why do you think this class is required for your degree?

For:

2. Why do you think this class is important for your degree would be a better question to ask students.

I think it's better to introduce quotation marks:

"Why do you think this class is important for your degree?" would be a better question to ask students.

Whereas in:

3. I would suggest that a better question to ask would be why we think this class is important for our degree.

It's more of a general statement so it's fine to exclude the question mark.

Anyhow, options (2) and (3) are definitely worded better than (1). Whatever you choose is fine and whether you not follow my suggestions for (2) and (3) is up to you.