Did you download the JRE offline version? I don't know what's going wrong for you...when you choose that installer, you should get a popup asking if you want to save the .exe file...once it's downloaded, go to where you've saved that file, double click on it & the installation should start

Whether it's got anything to do with your Bluetooth mouse I don't know...I don't use any Bluetooth devices.
Someone else might know.