First find the total of the 5 recorded circumferences: $12+12+16+18+22=80$. If the mean of 6 garden beds is $16$, then the total for all 6 must be $6\cdot 16=96$. So the sixth circumference is $96-80=16$. Check the range: the original minimum is $12$ and maximum is $22$, so the original range is $22-12=10$. Adding a circumference of $16$ does not change the minimum or maximum, so the range stays $10$. Therefore, the sixth circumference is $16$ feet.

First find the original total: $120+135+135+150+165+180=885$. After adding one more Saturday with 135 visitors, the new total is $885+135=1020$. There are now 7 Saturdays, so the new mean is $\frac{1020}{7}\approx 145.7$. Next, list the 7 values in order: $120,135,135,135,150,165,180$. With 7 numbers, the median is the 4th value, which is 135. So the new mean is about 145.7, and the median stays 135.

Adding the same constant to every value in a data set shifts the entire set without changing how spread out the values are. Standard deviation measures spread, so it stays the same.

The original data set has standard deviation $s$.
The new data set is formed by adding 3 to each value, so its standard deviation is also $s$.

Therefore, the correct expression is $s$.

The original data set is $2,4,4,6,6,6,8,8$. Its sum is $44$, so the mean is $\frac{44}{8}=5.5$. After adding one more $8$, the new sum is $52$ and the new number of values is $9$, so the new mean is $\frac{52}{9}\approx 5.78$. Therefore, the mean increases.

For the median, the original data set has 8 values, so the median is the average of the 4th and 5th values. Those are both $6$, so the original median is $6$. After adding another $8$, the data set has 9 values: $2,4,4,6,6,6,8,8,8$. The median is now the 5th value, which is also $6$. So the median stays the same.

Therefore, the statement that must be true is that the mean increases and the median stays the same.

The original data set is $5,6,6,7,8,10$. Its mean is $\frac{5+6+6+7+8+10}{6}=\frac{42}{6}=7$. Its median is the average of the 3rd and 4th values: $\frac{6+7}{2}=6.5$.

After removing 10, the remaining data are $5,6,6,7,8$. The new mean is $\frac{5+6+6+7+8}{5}=\frac{32}{5}=6.4$, so the mean decreases. The new median is the middle value of the 5 numbers, which is $6$, so the median also decreases.

Therefore, the correct answer is B.