I'll answer questions 1,2,3 and 4.
(1) How may I associate CPI to vehicle cost/price in dollars (USD) for a given year?
From the Federal Reserve Economic Data, we see that the base year is 1982-1985, where the CPI for new vehicules is 100. We can also estimate from other sources, that the average price of a new car during the base period was 20 000$ (I found data for average base cost, which over estimate the weight of notchback cars - I adjusted for luxury cars and other categories). If we compile those informations, we can derive the following formula for the price of new cars:
\begin{equation*}
P_{n} =\ 20\ 000\left(\frac{CPI_{n} -100}{100}\right) +20\ 000
\end{equation*}
Where:
\begin{gather*}
P_{n} =\ price\ at\ target\ year\\
CPI_{n} \ =\ target\ CPI
\end{gather*}
Let's experiment a bit. If our target year is 2021, the average CPI for new cars is 160, which means that the average price for a new car would be about 32 000$ (which is less that the actual average price). There's a few explanation for this divergence. The most probable answer is (in my opinion) that the consumer preference changed to premium cars and SUV, which are way more costly that the basic notchback popular in 1982-1985.
(2)Does the CPI value actually matter or is it the change over time that matters?
Both, as shown in the previous answer. The CPI number is important for comparaison and presentation. The difference over time is useful for calculations.
(3) How does one explain this rate of change in terms of dollars?
You can refer to the previous equation, but usually the link between CPI and price is the following:
\begin{equation*}
\frac{CPI_{n}}{100} =\ \left(\frac{Price\ at\ target\ year}{Price\ at\ base\ year}\right)
\end{equation*}
You'll find the same results using this equation.
(4) Is there a better indicator
For cars, yes. The CPI does not include change in quality and preferences. This leads, as I explained previously, to false estimation. To have a better estimation, you can use a Paashes Index, which takes into account changes in quantity and behavior. You'll find more information here: https://corporatefinanceinstitute.com/resources/knowledge/economics/paasche-price-index/
