I've repaired a number of statues, broken fountains, etc. there is a product called 'Gorilla Glue'. It's available at Home Depot, etc. ($5) Buy the smallest size (a bit goes a long ways) and don't use too much as it expands. It can go on wet surfaces and is incredibly strong.

Re your bird bath. If there are sizeable cracks, use a mortar mix ($6 bag) and apply a thin 1/4" light coat. 'If' the color isn't quite right then add a bit of color...the building stores have additives). There's also cement like products available for repairing basement leaks. These work fine. The ones you need to add water to are usually better than the ones that come ready for use.

It's surprising how many fountains and pumps have been left unused in backyards for years. I buy them up for a few dollars and most fix up in a jiffy.