Right, although the firm may have partnership agreements with its partner(s), the trader is a member of the LLC and signs an operating agreement.
Keep in mind that if you're removing liquidity on most trades by selling at the bid or buying at the offer, then as a general rule, you can expect add another $2 to $3 per 1,000 on that rate in commissions. That will put your true commissions at around $5 to $10 per 1,000. So for example, a new trader who does not add liquidity and does around 100k shares per month will pay around $500 to $1,000 in commissions alone! That does not include platform fees and professional data fees. Before you join a prop firm, it's best to evaluate an estimation of your true monthly costs, both fixed and variable, so you can define the amount of money you'll need to make on a monthly basis to justify the costs. If you can add liquidity to most of your trades, then you can greatly reduce your variable costs per month, and perhaps even get them close to zero. Those who ignore their variable costs will end up as "commission churners and burners" which is great for the firm, but not so great for the trader.
So if I trade with limit orders and let price come to me (i.e buying when there may be many sellers, or selling when there may be many buyers). Would that help provide more liquidity? However, do trades need to be flat EOD? Or can I use, say $25k on a $100k BP account to swing trade the position?
Limit orders (buy and sell side) will add liquidity and get you the ECN rebates, depending on the platform and routes they use. Regarding flattening trades by EOD, that's usually how it works. Regarding overnights, T3 obviously has traders who hold overnight, because the amounts at end of year are disclosed in their SEC.gov focus reports. I'm not sure how much capital you'd need to put up, so it's better to ask them.