11. (1) Let the weight of the fish at the end of the $n$-th year be $a_{n}$. According to the problem, the growth rate forms a geometric sequence with the first term 2 and common ratio $\frac{1}{2}$. Therefore, the growth rate in the $n$-th year is $\left(\frac{1}{2}\right)^{n-2}$, and $a_{n}=a_{n-1}\left[1+\left(\frac{1}{2}\right)^{n-2}\right], a_{1}=3 a_{0}, \cdots, a_{5}=\frac{405}{32} a_{0}$.
$a_{0}$ represents the original weight of the fish, so the expected weight of the fish after 5 years is $\frac{405}{32}$ times the original weight;
(2) Let the total weight of the fish at the end of the $n$-th year be $a_{n}$, and the total weight of the fish starts to decrease, then
$$
a_{n+1}=a_{n}\left[1+\left(\frac{1}{2}\right)^{n-1}\right] \cdot \frac{9}{10}, a_{n}=\left[1+\left(\frac{1}{2}\right)^{n-2}\right] a_{n-1} \cdot \frac{9}{10} .
$$

From the condition, we have $a_{n+1}<a_{n}$, and $a_{n-1} \leqslant a_{n}$, solving this gives $18<2^{n} \leqslant 36$, so $n=5$, meaning the total weight of the fish starts to decrease after the 5th year.
11. A fish farm raises fish, in the first year, the growth rate of the fish's weight is $200\%$, and it is expected that the growth rate in subsequent years will be 0.5 times the previous year's growth rate.
（1）After 5 years of breeding, how many times the original weight is the fish's weight expected to be?
（2）If due to environmental pollution, the fish's weight decreases by $10\%$ each year, then after how many years will the total weight of the fish start to gradually decrease?