I have used the Mosaic to New Raster tool and it works however the raster tif does not show in the layers or my documents, why is this happening and how can I solve this issue?
You can find where it is by right clicking on the "Output Raster Dataset" line in your result panel. you'll be prompted to add it to display or copy location.
EDIT : from your edit, it's your default Arcgis processing database.
If you have removed by mistake your layer and have the "Resulat are temporary by default" option in, it may be lost:
You can also try to Ctrl + click the minus sign to see all your layers more easily. It may be in your windows but in the middle of your other layers ?