While prospective fund managers are fundraising (but before funds are formed and operational), how do they make arrangements with advisors, venture partners, or other similar types of personnel?

Fund managers can discuss future arrangements verbally - however they should refrain from making any promises or commitments (verbal, written, or otherwise).

Particularly, fund managers should sign NOTHING - as a general matter, legal agreements cannot be signed on behalf of fund entities that do not exist. This goes for any investments intended to be warehoused as well - a prospective fund manager must sign those as an individual or on behalf of a wholly-owned entity the fund manager will invest out of.