1) Why not?
Remember, that you dont't make a didone minus the serifs, but also minus the high contrast.

2) Yes.
Take an ink pen, the one that pours ink on paper when you don't move your hand. Draw these letters with one second of debt.

1+2) Manage the resulting crisis, according to the effect that you want to achieve.

My feeling is that a ball terminal (or any particular terminal convention) usually exists not merely as a style of "decoration" but also a functional way to add a particular kind of weight to that stroke. And I can imagine an /a/ and an /f/ in the same font that would have rather different needs for weight at their tops. In that case, identical terminals for consistency's sake wouldn't be particularly desirable.

In my experience, a close look at successful fonts often reveals more inconsistency in terminal treatments than I expected to find.

How can it be a sans-serif typeface if it has balls?
Ball terminals are a kind of serif.

Look at Archer and Bodoni Egyptian.
They are monoline faces with ball terminals, but also serifs, slab in fact.
Imagine them without the straight serifs.

Perhaps something like Sari manages the integration, mixing balls with rounded "plain" terminals, due to greater contrast of stroke thickness.

But if you're following a hard-edged didone model, perhaps the answer is small balls.

Experiment and see what works!

Is it okay to use ball terminals on a sans-serif typeface?

It is OK if it looks good.

and 2. Say hypothetically I use a ball terminal on the letter 'f', does that mean …

Are you a student? If so, then go and study.

[i]Ball terminals are a kind of serif.[/i]
Indeed. But only when we trace the outline stroke. The skeleton of letters with ball and teardrop terminals usually behaves like that in a sans-serif.