Hardware-wise, you have 3 options. #1: It's perfectly fine to use Teensy as a component in your product. This makes sense at low volume or for a first run for demos, eval units, etc. #2: If you're making your own PCB, but at modest volume, we have pre-programmed chips you can buy. Using that chip and similar parts (the same crystal frequency) gives your board compatibility with Teensy Loader, so you can get your own hardware working without extra much extra design work. This is often a smart intermediate step from low to high volume production. #3: For high volume production, there are many solutions available on the market to directly program the chip on your PCB. These require up-front costs and work, but they are the lowest cost per unit. For AVR (used on Teensy 2.0), Atmel's AVR ONE might work. For Freescale Kinetis (used on Teensy 3.0), P&E Micro's Cyclone programmer is the preferred solution. The .hex file you used on Teensy can usually work when used with those tools.
Software-wise, most of the code PJRC publishes is MIT license to allow usage in close-source products, or a modified MIT license which requires special attribution only if you're making a development board (eg, a Teensy competitor) and publishing the source code. Obviously that doesn't apply if you're making a closed-source product. Some Arduino libraries are GPL which does not allow publishing as closed source. Ultimately, you should check the license on every piece of code that gets built into your application. Also, as an obvious disclaimer, this message is not "legal advice". For that, you'd need an attorney.
Busienss-wise, if you're planning to sell physical a product, I'd highly recommend focusing on customers and sales. Obvious as that sounds, I've seen many great ideas fail because the founder couldn't make the transition from focusing on engineering to sales and marketing. A big red flag is repeatedly redesigning the product, especially if the goal is cost reduction, before making many sales. When you have a lot of units sold, which might be Kickstarter, or a single large client, or the result of slowly increasing sales, then it can make sense to redesign. But if you don't have customers lined up, all the best engineering effort in the world won't add anything other than more red ink.