> Apple has violated Section 2 of the Sherman Act due to having a monopoly on Apple services?

Sort of. There are two possible avenues of attack here against Apple. And it depends on how the market is defined.

1: if the "market" is defined as you have, which is a "monopoly on apple services", then it absolutely true that Apple does have a monopoly on the specific market as defined by "Apple services", and I would accept 10 to 1 betting odds on that.

BUT, I think it is a bit of a stretch that the "market" will be defined that narrowly. Instead I think that the market will be defined as the smartphone market share of the USA.

2: If the market is defined as the smartphone market, in the USA, then the argument will be that Apple has control of ~50% of the market, in a 2 entity duopoly. It is a common misconception, that anti-trust law only applies in cases, of a overwhelming singular monopoly. Instead, anti-trust law, applies even in cases where there is not a singular monopoly, and the company in question only has significant market power.

Controlling 50% of the market share, is a bit on the edge of whether anti-trust law applies, or does not apply, as according to government guidance. So the case is far from a slam dunk, and I think that there will be interesting arguments brought up in court.

But, even though Apple has less market share than, say Microsoft did, when Microsoft lost their anti-trust case, I think that Apple's actions are significantly more restrictive than Microsoft's was, and thus this contributing factor will push them over the edge into losing the case.

I expect that this case will be a landmark case, that will determine future court actions, and will be even more significant than the microsoft case was.

No, Apple, among other things, has violated the laws against anticompetitive behavior by attempting to exert its market dominance in one market (iPhones) over a separate market (app stores) by engaging in punitive and market-distortive actions against potential competitors.

Similar antitrust violations of the same nature: iMusic vs Spotify, iChat vs Hey/other chat programs, Apple Webkit vs all other browsers.

I would have included Apple Pay but in that instance Apple lost, largely because their actions in other markets made it extremely undesirable for merchants and payment processors to get behind Apple's vision of Apple Pay in which Apple skimmed X% for providing absolutely no value to the transaction. In fact, so many retailers found Apple to be an undesirable partner that a number of major retailers disabled Apple Pay integration on their NFC-capable payment terminals. For example, most Kroger locations (like Ralphs) take Google Pay, Samsung Pay, Garmin Pay, and most other app-based NFC payment methods...but not Apple Pay. (Apple's situation is similar to American Express, which also charges significantly higher rates to retailers than its competitors, but unlike Apple, Amex actually processes transactions and theoretically provides valule to retailers, just not enough to justify its Appleesque rates.)