Hi Denise,
We typically recommend that an education foundation not take on the fiduciary responsibility for booster clubs or other parent organizations.  Primarily, booster club leadership changes frequently and with the education foundation processing their funds, the foundation takes on the liability of all actions taken by the booster club and the subsequent fiscal actions by another board that the foundation has no control over.  
If the education foundation were to simply take receipt of the funds and "house" them for the parent organization, the foundation has still taken on that liability of the donors/members of the booster club or parent organization.  
We have also seen this type of arrangement go very wrong if the foundation is involved with the parent organization and they do not like something the foundation has done - either receipt of funds, disbursement of funds, acknowledgement of funds, investment of funds, etc. When parents get upset, it puts the foundation in a very difficult place.
Even for education foundations that are charging an administrative fee to process the funds, the risk taken on and the benefits received do not tend justify this action.
As far as the logo, there are education foundations that use the logo of the school system - typically when selling items or promoting something that the foundation if doing to solicit funds for the school system.  Many districts have their logo trademarked, so the education foundation would need written permission to use the logo. Even if the logo has not been trademarked, it is important to have written permission from an authorized district representative.
Hope this helps and thanks for posting.
 
Hi Denise! Many of us are district employees and have other assignments outside of the Education Foundation (which is why it's so challenging to compare positions and salaries, but that's another topic....). My title is Director of Corporate & Community Development, with 49% of my position's time devoted exclusively to the EF. The rest of the time I work with district fundraising and sponsorships, partnerships, and parent-led organizations that support the schools (PTA, Booster Clubs, etc.)
I advise our fundraising groups and maintain data on what fundraisers are going on, but I never touch their funds. I wouldn't want the liability for that function, as Laurie explained previously. 
We have a district branding policy regarding the use of our logo, but we do allow our supporting organizations to use it. It is not trademarked. We've worked really hard to standardize the use of corporate sponsor recognition on campus facilities, trailers, etc. through our public relations department. I can share that if you are interested.