How much collaboration is reasonable for a Two-Headed-Giant draft?
I recommend just straight-up reading the MTG Tournament Rules. You certainly don't need to do all of this stuff for a &quot;casual&quot; draft, but it'll give you some good ideas about how to run things.
As Two-Headed Giant draft is actually an officially supported format, the MTR includes specific guidelines on how to run it. DCI recommends drafting as a team, then building decks from one shared pool:

9.6      Two-Headed Giant Limited Rules
All the rules for Limited Tournaments (Section 7) apply, except as described below. The DCI
recommends that each team receive eight boosters per team for
Two-Headed Giant Sealed Deck tournaments and six boosters per team for
Two-Headed Giant Booster Draft tournaments. For the recommended
product mix for the current block, refer to Appendix E. Cards not used
in a team’s starting decks are considered a shared sideboard by the
two players that both players can access.
9.7      Two-Headed Giant Booster Draft Tournaments
Teams (not players) assemble into random drafting circles (called pods) of
roughly equal size at the direction of the Head Judge. Teammates sit
next to each other. Tournament officials then distribute identical
booster packs to each team in the pod. After opening and counting the
cards in their first pack, the team chooses two cards from the booster
pack then passes the remaining cards face down to the team on its
left. Selected cards may be placed into one or two piles. The cards
chosen are not assigned to a particular player; they become part of a
pool out of which both players will build their decks. The open packs
are passed around the drafting pod—with each team taking two cards
from each before passing—until all cards are drafted. For the second
pack, the direction of drafting is reversed as usual. Thus, the
overall draft direction is left–right– left–right–left–right.

Generally, there are no prohibitions on communication between teammates; tournaments instead use time limits to discourage analysis paralysis:

4.4     Team/Two-Headed Giant Communication
Members of the same team may, at all times, communicate between one another verbally. This
includes during play, during drafting, and during deck construction of
Limited tournaments. However, team members that have an opportunity to
acquire hidden information (e.g. by speaking to spectators following
their own match while a teammate is still playing), are restricted
from communicating with teammates for the duration of that match.
Prohibitions against written notes of any kind during drafts apply to
team drafts as well.

If you're playing without judges, I encourage working out some kind of procedure for handling slow play within your group.