Go to the FCC's website and download Part 15 of their rules and regs... that's the section dealing wiht low-power transmitters/receivers. By getting an item tested (you get a company/item ID # when it passes) you are proving to the FCC that your product fits several rules, such as total/average transmit power, transmit time, etc.
Using the chips is only half of the battle. You could design anantenna system that works so well (by accident), you crank out too much power. The receiver can use a wire/whip antenna, but you have to understand the compromises in using one over another design, as well as how to design it (it's not just a simple piece of wire cut to any length)... any receiving element can inadvertantly become a transmitting element, therefore you need to test it for such.
For a handheld remote, you can't use a wire for the antenna, you have to use a PCB patch antenna, and that's where the fun starts. You can find design guidelines for how to create them, but you're not likely to find a pre-made solution, and lots of testing time will have to be invested to get it to work.
Range depends on power, but again, that's regulated by FCC rules. UHF stands for Ultra-High Frequency, which is a band of RF. It can go through walls, IR cannot.
If I remember correctly, my last reading of the rules states up to two prototypes can be made/used and may not be sold. Because of your questions about UHF and IR, my guess is you're not highly electronics literate... that being the case, I would suggest having someone else work on this portion of the project for you, or give it up altogether. There are too many unknowns in this type of project for you to learn in a reasonable period of time. Maybe in 6 months to a year with a lot of reading you could begin some basic designs, but it doesn't sound like you're at that point yet.
Good luck!