Haven't gotten a reply, but figured I'd ask a few things here.
Give it time, not everyone checks theses forums 24/7. I don’t know about others, but I typically hit the forums maybe 2 times a day max unless I am watching a specific thread.
You do not indicate your general location, but I will assume you are in the US and my answers will be predicated on that assumption. Different nations have different requirements.
Do you always need a ham license to place a transmitter for a fox hunt type game?
The need, or not, for a license to place a transmitter will be driven by the service the transmitter is in. If the transmitter operates within ham bands then a ham license will be needed and certain performance limitations and transmission requirements will need to be achieved. If the transmitter is in a service that does not require a license, for example FRS, then a license is not needed (I do not know if the FRS regulations allow unattended operation, that is something that would need to be confirmed, just using FRS as an example).
A Part 15 legal transmitter would not require a license.
If this is not making sense to you, it might help to understand that the “regulations” that control radio transmissions are divided up into multiple parts, each part has separate requirements. For example Ham radio and CB radio are not the same, and have different requirements. As does Public Service radio, Family Radio Service, MURS, etc, etc.
How do you pick out a frequency to use? Can you make up your own? How many digits can you use?
The frequency of operation would be a function, again, of the particular service the transmitter is in. Each service typically has bands the transmitters can operate in, with many services being specifically channelized, meaning you would have to be on one of the specified frequencies. Using CB as an example you would be able to select from one of 40 channels in the 26965 kHz to 27405 kHz range. Other services (ham radio, for example) would just give you a maximum and minimum frequency, and you can select any frequency between those points (within certain guidelines).
Please clarify what you mean by “How many digits can you use?” 26.965 MHz, 26965.0 kHz, and 26965000 Hz are all the same frequency, and are all CB channel 1.
I've seen these big antenna's, but are there small antenna's that can be used from a car and then on the ground while searching for the transmitter?
Antenna selection for Fox Hunting is a huge juggling act. As a general rule the “size” of an antenna is a function of the frequency used. However there are several compact designs that can be used for RFDF, assuming the user is willing to accept the performance limitations.
In other words, yes, you can probably find a small antenna to do what you want, but this is not a simple question, it cannot be answered quickly, easily, and with detail in few lines of information. And based on your other questions I assume you do not have adequate background to understand the possible answers. This last is not a slam on you in any way, I am only saying antennas for RFDF can range from very simple to get quite complex and antenna selection can be a balancing game of compromises, and you sound like you need more background before you can start to understand the factors.
Is it possible to monitor the transmitter from a home area far away to see if a team has found it?
The possibilities are only limited by your imagination, technical background, and the depth of your pockets. If you wanted to, for example, you could absolutely put a camera monitoring the transmitter location, and monitor the site from any location you wanted.
T!