what squad mode abilities do we get? I see our oath that we take determines some of them and I know we also get access to chapter squad mode abilities of the leader, but do we get squad mode abilities from somewhere else as well? Where in the book talks about this stuff?

Each individual space marine knows all of his chapter's squad mode abilities. The Kill team gains, and any character in the team may use, the Codex squad mode abilities granted under the oath the team takes at the start of the mission.

All the information you need to know about squad (and solo) mode abilities are on pages 213-225 of the main rulebook. Page 219 2nd column under the headings, "Gaining Squad Mode Abilities," and, "Using Chapter Specific Abilities," cover which abilities are available to the kill-team and characters.