There are two different TransAmerica Trail routes, one for bicycles and one for motorcycles. The acronym "TAT" almost always means the motorcycle route. I assume that this is not the route you are taking, so a better name is either "TransAm" or "TransAmerica" or, in this audience, "TA" is usually clear.
There are not many McDonald's on the TransAm. That's probably because most of the towns the TA passes through are too small to justify a McDonald's. Nevertheless, you can find Wi-Fi in a lot of other places. I would sometimes just wander around town checking for signals from open networks and then walking towards them to get a stronger signal. I used a lot of signals standing outside of buildings closed for the night. You won't find a signal every day, but you will find one every few days.
May through October in the U.S., especially on the TransAm, is usually suitable for camping, cold in some spots and hot in others, but rarely so cold or so hot that you cannot camp. How much or little you camp depends on you. You can camp easily camp 90% of the time if you want, and 100% of the time if you are a bit creative. If you don't mind camping, it's a great way to save a lot of money. Having camping gear and being able to camp at least some of the time increases your flexibility greatly on the TransAm, because finding indoor sleeping every night is a struggle (although possible if you're committed to it).
Warm Showers provides a nice break from other lodging options, and is a great way to meet interesting people.
Studying English is good, as you won't find many people along the TransAm who know Korean.
If starting the TransAm in the East, it will be much, much better to start in May than to start in August.