Can we use those companies' projects and logos in advertisements without permission? Or is this trademark infringement?

It would be trademark infringement to use the names and logos of other companies in advertising. Depending on how the trademarks are used, it make be able to avoid paying fines if it constitutes fair use under the comparative advertising exception. Kind in mind, this is an affirmative defense which does not allow prevail and will not prevent the trademark holder bringing suit.

Yes, your client would need permission from all of the companies whose materials he uses. To be honest, they are not likely to give their permission for their company to be part of his ad campaign. However, If he wants to start a Made in the U.S. campaign and it picks up steam, they might sign on. A lot will depend on his track record, connections, background, and having the right team, including a good lawyer.

Generally, no, you can't use registered trademarks without the permission of the trademark owner.