Chinese languages

I'm a beginner in Chinese, so I'm sorry if this is a silly question - Is it acceptable to mix traditional and simplified hanzi together in the same sentence? Do all characters even have both a traditional and simplified version?

Mixing traditional and simplified Chinese is not proper. Whether to use traditional or simplified is determined by the country. Mainland China uses simplified. Taiwan, Hong Kong and overseas areas in Europe and US use traditional.
There are only a limited number of characters for which there is a simplified form. The "not simplified" forms in simplified Chinese are just the original traditional forms.

Cheers