You can live for long periods on juice alone, but you should use a variety of foods to make the juice. Above ground veggies should be the source of the majority of your juices if you want to lose weight.
Loose teeth are generally a bacterial infection in the mouth. This would benefit from overall improved health, but you also need to do more than brush your teeth a couple times a day if you want to avoid losing them.
Do you smoke? That causes loose teeth by poisoning the gum tissues.