For simplicity, let's start by just considering cash back. In general, cash back from credit cards for personal use is not taxable, but for business use it is taxable (sort of, I'll explain later). The reason is most personal purchases are made with after tax dollars; you typically aren't deducting the cost of what you purchased from your personal income, so if you purchase something that costs $100 and you receive $2 back from the CC company, effectively you have paid $98 for that item but that wouldn't affect your tax bill. However, since businesses typically deduct most expenses, that same $100 deduction would have only been a $98 deduction for business tax purposes, so in this case the $2 should be accounted for. Note, you should not consider that $2 as income though; that would artificially inflate your revenue. It should be treated as a negative expense, similar to how you would handle returning an item you purchased and receiving a CC refund.
Now for your specific questions:
Part 1: As a small business owner, I wish to attend an annual seminar to improve my business. I have enough credit card reward points to cover the airfare, hotel, and rental car. Will those expenses still be deductible at the value displayed on the receipt?
Effectively no, these expenses are not deductible. If you deduct them they will be completely counter-acted by the "refund" you receive for the payments.
Part 2: Does it matter if those points are accrued on my personal credit card, rather than a business credit card?
This is where it gets hairy. Suppose your company policy is that employees make purchases with their own personal credit cards and submit receipts for reimbursement. In this case the employer can simply reimburse and would not know or care if the employee is racking up rewards/points/cashback. The trick is, as the employee, you must always purchase business related items normally so you have receipts to show, and if you receive cashback on the side there seems to be a "don't ask, don't tell" rule that the IRS is OK with. It works the same way with heavy business travelers and airline miles- the free vacations those users get as perks are not treated as taxable income. However, I would not go out of my way to abuse this "loophole". Typically, things like travel (airfare, hotel, car rental, meals) are expected. But I wouldn't go purchase 100 company laptops on your personal card and ask the company to reimburse you. The company should purchase those 100 laptops on a company card and effectively reduce the sale price by the cashback received. (Or more realistically, negotiate a better discount with your account rep and just cut them a check.)
Part 3: Would there be any difference between credit card points and brand-loyalty points? If the rental car were paid for with points earned directly on the rental car company's loyalty system (not a CC), would that yield a different result?
There is no difference. Perhaps the simplest way to think about this is you can only deduct an expense that you actually incur. In other words, the expense should show up on a bank or CC statement. This is why when you volunteer and work 10 hours for a charity, you can't call that a "donation" of any amount of money because there is no actual payment made that would show up on a bank statement. Instead you could have billed the charity for your 10 hours of work, and then turned around and donated that same amount back to them, but it ends up being a wash.