Open sourcing a project with free assets downloaded from Unity Asset Store

That depends on the license of the free assets. The standard asset license does not permit redistribution. However, a publisher could choose to use a less restrictive license. If that license permits (e.g. CC0 license) then you should be fine. In most cases you can't though. You need to check the license of each individual asset.

What you can do instead is maintain a list of all assets you need to download for the project and let each participant download them from the asset store themselves. As the GUID:s will remain the same for each asset metafile all references should still work. Bonus point if you can create an editor scripts which automatically downloads the assets needed when you load the project :)

You cannot redistribute the source of any assets downloaded from the asset store. Whether they were free or paid is irrelevant. Read section 2.2 of the EULA: https://unity3d.com/legal/as_terms

"Licensor grants to the END-USER a non-exclusive, worldwide, and perpetual license to the Asset to integrate Assets only as incorporated and embedded components of electronic games and interactive media and distribute such electronic game and interactive media. Except for game services software development kits (“Services SDKs”), END-USERS may modify Assets. END-USER may otherwise not reproduce, distribute, sublicense, rent, lease or lend the Assets."