Are all objects fixed in gender?
For example, are ALL potatos feminine? Or, is it possible to change "papa" into a masculine form?
Grammatical gender has little to do with natural gender (male/female). In the case of people and some (usually domesticated) animals, they coincide but for the most part, there is no logic to grammatical gender. In many cases a word is masculine/feminine because it had that gender in Latin. Of course that may prompt the question "Well why was it masculine/feminine in Latin?" Grammatical gender has more to do with the way a word sounds than with the meaning of the word.
Like socceryo3 said, nouns have fixed gender. But there are some cases, like policía, where it can be a bit confusing out of context. La policía can mean the police force, and it is femenine. La policía can also mean a police woman, which is obviously also femenine. But el policía means policeman, masculine. But they don't change. You can't have masculine potatoes.
Find me a male potato. Hahaha.
But in all seriousness, yes they all have a gender. It's not any kind of exact science at all, and it doesn't mean the object IS a girl or a boy. La persona, the person, can be a man or a woman. You can refer to a guy as una persona. Doesn't mean he's a girl or that you're calling him that.