Lights not working after replacement
There must have been some wire splices in the junction boxes of the upstairs lights that were disturbed when you installed the new fixture.  Take the last fixture down (the one installed before the downstairs lights failed) and look at the other wire connections.  If there is a bundle of wires (or two bundles), take off the wire nuts and make sure everything is tight and twist on a new wire nut.  Of course, all the power should be off when you do this as you will be in contact with multiple wires.

If you don't find any bundles, take down the next fixture you installed and check that junction box.  Home electric fixtures are never wired in series, so one fixture working shouldn't depend on another being installed.