You can equip gear in all slots regardless of the retainer's level, so long as your retainer meets the gear specifications like race and gender (if applicable), class, and level.

Does equipment matter? I'm not entirely sure about this one actually. The venture system may just be a shiny way to display your old gear, or gear may actually have some effect on the results. The system hasn't really been out long enough for people to test this though because :

Ventures require 18 (real life) hours to complete. If you assign your retainer more ventures before their current venture is complete, it simply abandons the previous venture and you have to pay for a new one.

You can obtain the rewards of your retainer's venture only after it is complete by clicking "read venture report" (or something similar) in your retainer's command menu. This will award both your retainer the exp, and you the items gathered during their venture.