1. I would translate it as "stripe", very plainly. The recent total solar eclipse (Sonnenfinsternis) has moved along on a diagonal stripe on the very edge of Europe, like a grain harvester that harvests a stripe on a field...
2. This phrase seems to be unrelated to the first one; this is a "workaround" translation of it:
"Investigations on how it came to happen have been commenced (as somebody stated)"
It is in indirect speech (indirekte Rede). This here would be Perfekt with direct speech:
"Es sind Untersuchungen zum Hergang eingeleitet worden"
if you replace "sind" by "seien" you make it clear that you are quoting somebody.
Example for direct/indirect speech:
Herr Professor Brinkner sagte mir: "alle Praktikumsplätze sind schon vergeben"
<-> Herr Professor Brinkner sagte mir, alle Praktikumsplätze seien schon vergeben.
You would quote him indirectly when mentioning this statement of his in an email.