Is he reffered to as patient Zero due to the fact that he is the first guy that Suresh interviews?

Suresh called Sylar the 'first of them'. We don't know what all he and Sylar spoke about, so, if Sylar had his abilities since being a child, he could be the first. As of right now it's impossible to determine.

I think the key word is PATIENT.

I bet Chandra realizes that Sylar was the first human to be able to "force" the evolutionary process.

Hence he is not Hero Zero, he wasn't the first person to display a power. He was the first person to manipulate his genetic code to manifest a power. That makes him Patient Zero.

How did he force the process? You are assuming he has no power to begin with.
Sylar himself states that he can "feel them." Thats a power. Sylar also states that he can see how things are supposed to be put together and that "they" are broken. He can see the broken pattern in their brain by looking inside it and adjust his own brain via his power to mimic their "settings" thus gaining their powers. In effect mechanically adjusting himself to mimic them. Thats a heck of a power. That is why he is killing people.

Therefore he is Chandra's first subject, his first patient, the one that begins his actual "hands on" study...Sylar is Patient Zero.

I think that's exactly right. Nothing to add.
We already know he can't be Hero Zero (nice, I haven't seen that one before ) and since we know he's a rather young guy he can't be some kind of walking virus (there's a theory I liked about this) back in the days.

Sylar is the first to "demonstrate" his powers to Chandra as well, with the glass flying off the table. Until then, it was all theory to Chandra. Therefore, Sylar is "Patient Zero" I think.

According to Mohinder, Chandra Suresh did go to Queens to find Patient Zero. I'm still wondering if Sylar is that person Dr. Suresh was searching for. HRG made it clear that there were others before Sylar that have superhuman abilities. Could there be someone else that is patient zero?

The term that Chandra uses on the show "Patient zero" means something specific. The term patient isn't significant in itself. Patient zero is being misused in the show. The term that should be used is index case. An index case is just the first patient to be examined in a study of an epidemic event.

But Sylar forced the evolution in the way that he effectively took a power from someone else. If he is truly piling up powers to his heart's content he's creating a new generation of superheroes which is not meant to be, purely by nature's design. He's artificially engineering himself. Like he's a god. It's some kind of new disease. Patient Zero.

I agree, it's reaching a bit.
You could just say he's Patient Zero because he's the first one Chandra ever sees using his powers. The samples he talks about in the journal were just research.

Anyway, I like the way to look at it from another angle. It's probably not what's intended with the term Patient Zero, but it fits pretty well.

True, but the two terms are commonly confused by laymen, and Chandra is not a specialist in an area where it would come up often.