Paul says that after his death Jesus appeared to Peter, to James, to the Twelve, to 500 other members of the community, and to all the apostles. "The Twelve" is stated in a way that assumes the audience will know who they are, and they are grouped together with those who were followers of Jesus. I'm all for questioning common assumptions, but who are these twelve supposed to be if not the Twelve that the Gospel authors will later try to identify (even though they give different rosters).
Only if you're not familiar with Paul. In his language that only means one thing. (E.g. "ἀλλ’ ἡμῖν εἷς Θεὸς ὁ Πατήρ, ἐξ οὗ τὰ πάντα καὶ ἡμεῖς εἰς αὐτόν, καὶ εἷς Κύριος Ἰησοῦς Χριστός, δι’ οὗ τὰ πάντα καὶ ἡμεῖς δι’ αὐτοῦ."—1 Cor. 8.6.)
Not so much. For one thing, Peter and James are supposed to have been direct students of Jesus. For another, Paul uses the term apostle to refer to a privileged subset of Jesus's direct disciples, those whom he sent out into the world to teach others in turn. The fact that Paul claims to be one of those despite never having known Jesus in person is extremely important to understanding his program, as well as the reason for his friction with Peter and James. In short, not all disciples are apostles, but all apostles in this context are disciples.
It gains that title in the late 2nd century. The mainstream scholarly view is that it was composed near the end of the 1st century, around the same time and by the same author as the Gospel of Luke. That means it's not an ideal historical source for the particulars of the time it's describing, and the author's knowledge of Paul is flawed enough for us to reject the tradition that he was actually the Luke who was Paul's disciple, but dismissing it as nothing more than propaganda is not something an actual historian would do. Like the Gospels, it's a complex work that partly reflects the author's understanding of the time and events in question, and partly represents an attempt to construct the narrative to reflect his contemporary concerns. It shouldn't be taken at face value as a record of events, but it's not without its uses.