Check for any scale range defined for the visibility of the layer (Layer Properties > General tab).
For the ArcMap crashing issue due to ArcToolbox, try https://community.esri.com/docs/DOC-7545?sr=search&searchId=02a9bbe3-6164-4576-9549-861bfc8df14e&sea... especially https://community.esri.com/docs/DOC-2121?sr=search&searchId=e0563cf0-99f7-45d4-b5f2-7b8eb9b55e03&sea....
If the issue persists, you might need to contact Esri Tech Support to have a closer look into the issue.
....when Itry to project the shapefile again,...
my guess is since you mention projecting again, that the shape in question was projected before this started happening. It may help others to know
As far as ArcCatalog crashing, I second Jayanta's suggestion to reset your profile.
Try running the Check Geometry Tool and if anything is found, Repair Geometry Tool (on a copy of the data). Also, try deleting and recreating the spatial index.