Myopia will not get better naturally as people age. If you are still young, your prescription will still change or get worse until the late teens and then it usually stabilizes. Some people become less myopic in their forties due to relaxation of the ciliary muscle, usually by less than 1D. Some get more myopic due to increase in density of the lens. Some don't change.
That depends. It is said that vision can change with the time passing by. Some will get slightly better. However the overall trend is to get worse. So as far as I'm concerned, it may depend on the protection you did to your eyes. In everyday life, it is recommended to eat more vegetables and fruits to supply nutrition eyes need, regularly do eye exercises and avoid reading, watching TV or working before computers for a long time without a rest. In general, take good care of your eyes at any time.
Ah, I can't tell you whether your father was right. Because if you want to make his words right, I think it should be get old instead of grow up. Maybe you are a teenager now, so if you don't protect your eyes, the prescription will worsen dramatically. But why I said myopia will be better when you are old? Let me figure out it. Myopia means eyeballs get to protrude, so the images presented are in front of the retina and presbyopia is this kind of vision problem that the images will be presented in back of the retina. So, if you suffered from myopia, your prescription will be cancel out a part by the presbyobia when you are old. But if you don't protect when you re young, this is not going to happen. So, you should love your eyes and protect them in the daily life.
Myopic degree won't change with age. But hyperopia degree is possible to drop. With the aging, the elasticity of lens will be weakened gradually and this will lead balancing out the myopia. That means if you suffer the moderate prescription, you can take off your glasses when you are old. However, if you suffer heavy prescription, you will still wear your myopia glasses.