I think, based on your translation, that you're using the Perseus version of the text, which is Godley, 1920. So for simplicity's sake I'll use the greek from the same edition as available on Perseus if I need it.

To understand the context of Herodotus' portrayal of the Phoenicians you'll need a bit of context around the whole thing.

Herodotus' histories are pretty wide ranging, with plenty of diversions along the way to talk about things like local customs. In broad strokes, however, its an attempt to document the Persian Wars fought between many of the Greek city states and the Persian Empire in the early 5th century BC.

In some ways, his portrayal of the conflict is one of the Greek states vs the 'other'; the other being a bit of a nebulous concept that can more or less be thought of as non-Greek. He frames the conflict as something of an east vs western/Greek culture, also suggesting at certain points that the root of the ultimate failure of the Persians is in some way due to environmental differences between the Greek and Persian peoples.

Part of his account is trying to establish some kind of causality or origin point of this series of conflicts, which is where your quotes come into play. In Herodotus 1.1. the conflict he is referring to are these Persian wars.

When he refers to Io, we probably shouldn't consider her a historical figure, but more of a mythological one. That is to say, the historicity of these events is highly dubious. In any case, Herodotus considers this a precursor to the later conflict. As you've read, Phoenician traders seized a number of Greek women. In retaliation for the seizure of Io, an unspecified group of Greeks counter-kidnapped Europa, the Phoenician king's daughter (Herodotus 1.2.1). After this, a group of Greeks made their way to Colchis and abducted Medea (Herodotus 1.2.2.) Incidentally this is the same incident that Apollonius of Rhodes depicted in his epic 'Argonautica' (Though in that version, she came willingly rather than being kidnapped).

Herodotus then connects this incident with Alexandros, son of Priam (otherwise known as Paris) and his decision to kidnap Helen of Troy, setting off the entire Trojan war. (Herodotus 1.3.1.) Notably, other portrayals of the Trojan war suggest similar thoughts about the 'non Greekness' of the Trojans.

In this way, Herodotus depicts Io as the first in a series of tit for tat actions between Greeks and Eastern civilisations, setting up the Persian wars as another incarnation of this.

As for your first point about the confusion over the Phoenician travel arrangements, the Greek given is "ἐνθεῦτεν δὲ ὑπερβάντες τῆς Συρίης οἰκέουσι τὸ παρὰ θάλασσαν" ( I hope the Greek characters show up, if not I'll try and make an edit.) Godley translates this as "they crossed from there and now inhabit the seacoast of Syria." Its a very slight touch too loose a translation for my liking but I don't think it makes any material difference. The relevant part of the Greek is "ὑπερβάντες" -crossing over. According to the LSJ lexicon, this verb can be used with bodies of water, such as crossing a river. In this case, however, it seems likely that Herodotus is just referring to them crossing over the stretch of land between their original home and the Syrian coast. Indeed the LSJ suggests that Herodotus elsewhere uses this verb with boundaries/landmarks (Hdt.6.108). So ultimately I think it likely that he's just saying that they migrated to Syria by land.

I hope this makes sense/helps.