I'm not sure what a semi-trailer is, but I would imagine a tow truck could help with your problem.
A Toyota Tercel is not designed to pull a truck on a trailer. This vehicle has a very low tow capacity at about 800 to 1200 pounds depending on the model.
If you look on your back bumper they may be a rating on how much your truck bumper can safely tow.
To tow an exhibition trailer, a large truck and hitch will be required. In a general sense, a medium duty truck is required. The best way to describe this is the average tow truck that is used to repossess or tow away standard vehicles.
A heavy duty tow truck
Straight truck is a single vehicle; i.e., there isn't a trailer in tow.
How much a tow truck can tow depends on the kind of tow truck or tow truck chassis is used. A few examples of types of tow trucks are boom, hook and chain, wheel lift, flatbed, and integrated.
pull it out with a tow truck
If you mean hooking a small trailer behind a bigger trailer behind your truck, no. You can only triple-tow in certain states and provinces and only if the first trailer is a fifth wheel.
No way of knowing this without knowing the dimensions and weight rating of the trailer.
Yes, just drive a little slower. Also be sure your transmission has clean fluid and is full. I would not tow anymore then about 3000lbs.
Probably not. Some people use smaller vehicles to pull Brenderup's, a lightweight trailer, but it makes me nervous. I recomend a full-sized pickup that is equipted with a tow package. You need substantial weight to safely pull your horse and trailer. The tow package gives you extra braking power and a heavier, secured undercarriage for a bumper-pull trailer. Make sure you have an expert check your hitch to make sure it is strong enough to pull something as heavy as a horse and trailer.