I am resident in the USA.
If I hold 50% shares on a foreign corporation in a beneficial tax regime, according to the US CFC rules I will own a controlled foreign corporation (CFC).
Would I be liable for tax on the 100% income earned by the company or just on my share of the corporation?
On the share that is liable, would I pay US corporate tax? Or would I pay tax as US individual on that profit (such as dividends)? Could I take tax deductions on my share?
CFC related rules are complicated, and penalties for non-compliance are steep. I suggest hiring a professional (EA or CPA licensed in your state) who has experience with CFC and other international issues (including tax treaties relevant to the countries involved).
You would file form 5471, and probably be a category 4 or 5 filer. You can start by reading the instructions I linked to that form, and try figuring the answer to your question out. I would suggest not trying this on your own.