A conversation that I can imagine being quiet common (especially in our house!) might be:

Kahve istiyor musun?
Evet lütfen. Siyah kahve istiyorum.

Three questions:
1. Is it correct?
2. In a friendly situation would you say "do you want" or is there a more informal "would you like"?
3. In black coffee (without milk) "siyah kahve"?

You did a good conversation, with no mistake. Well done.

Yes, in a friendly situation

"Kahve istiyor musun?" or "Kahve ister misin" (this one is used more for offers)

Yes, for black coffee it's siyah kahve, but as there're two kinds of coffees in Turkey, Turkish coffee and Nescafe,wWe usually use nescafe.

A usual conversation:

- Nescafe ister misin?
- Evet,lütfen. (Evet, isterim, sağol)
- Sütlü mü, sütsüz mü?
- Sütlü .
- Şekeri nasıl olsun?
- Şekerli/ orta / şekersiz.

Nescafe ister misin?
Is the -er suffix the aorist tense or something else?

Yes, aorist tense. For wishes it's mostly used. For example:
-Nereye gitmek istersin? Sinemaya mı, tiyatroya mı? Where do you want to go? To cinema or to theatre?
-Sinemaya gitmek isterim.


Şekeri nasıl olsun?
"How many sugars?"
Where does olsun come from?

Maybe it was not good to give this sentence, it confuses you. It's like "how about its sugar?"
olmak = to become,
Şekersiz olsun: let it be without sugar
I don't know how to express "olsun" in a question in english.

Why not:
"kaç tane şeker?" or "ne kadar şeker?"
Yes, these could be also but şekeri nasıl is preferred, because it may be without sugar too.

Şekerli/ orta / şekersiz
What does orta mean?
orta is average, middle. not with too much sugar, just average.

Can the -li and -siz suffixes be applied to any noun to mean 'with' and 'without' or are they specific to only certain things?

Could I say:
bilgisiz gitiyorum
"I am going without knowledge"

yes, I think it can be applied.

Bilgisiz is fine.