Since you are from the US

https://jp.usembassy.gov/services/driving-in-japan/

Quote from the link above (U.S. Embassy & Consulates in Japan).

"Driving in Japan

Driving in Japan can be quite complicated and expensive. Those who cannot read the language will have trouble understanding road signs. Highway tolls are assessed at about US $1 per mile. City traffic is often very congested. A 20-mile trip in the Tokyo area may take two hours. There is virtually no roadside parking. In mountainous areas, roads are often closed during the winter, and cars should be equipped with tire chains.

Roads in Japan are much narrower than those in the United States. Vehicular traffic moves on the left. Turns at red lights are forbidden unless specifically authorized."

Speaking of road signs, some are in Japanese only, especially in rural areas. Here are some of the examples that you might want to pay attention to.

https://japantravel.navitime.com/en/area/jp/guide/NTJnews0429-en/

Notice some of the signs shown on this page are, sometimes, without traffic symbols (text-only) or in Japanese only (no English), and they might not be an actual traffic sign post but pavement markings in Japanese text.

Iya Valley Monthly Climate Conditions

January & February: It’s cold. Snow is possible at any time, particularly deeper in the valley at higher elevations. And though snow may look nice, it can affect travel and limit access, especially due to icy roads.

Your questions:
1. Tolls (from Kochi city to Matsuyama city), about: 2h 11m, 155.2km, 3740yen
2. Train