Hypothetically, lets say the prop firm takes 50% of the gains, and you made $100,000 in gains trading futures, how much makes it back to you after the firm gets their cut, taxes you pay on cap gains and as an independent contractor, etc.?
The prop firm at the end of the year will issue you a 1099 or similar form for your profits made and you pay taxes on that amount as one of your Schedules. Taxes will most likely be ordinary income on short term cap gains but could be different depending on what product you traded (some have a short/long split. Also the prop firm does not deduct taxes, you will receive the gross income amount minus fees and the bigger question is what restrictions you have on withdrawing winnings. So if you make $100,000 net after commissions then your account will show your profit share is $50,000. You can take the whole $50k if the firm allows but taxes are your own responsibility April 15th.
But will I owe taxes on the $100K with just $50K in income, or do I just pay income and cap gains taxes on the $50K?
You need to ask if they issue you tax form 1099 or K1. K1 would be broken down into short/long term and other profit/loss/credit/deduction amounts. 1099 would be ordinary income. In either case, You pay taxes on your take. With possible deductions. If a salesman makes a 1M dollar sale and is paid a 10% commission, the salesman owes his share of tax on the 10%, not the 1M. If the salesman is also a shareholder or has some form of ownership in the company, there may be other taxable income/loss/etc which are the salesman's responsibility to report.
When you file taxes, you can also deduct seat cost or office cost, data and subscription fees and margin interest cost etc.