Comparing proportions between multiple groups - Fisher's exact test

I have a simple dataset on reproductive success of a certain plant species. Reproductive success was defined as a proportion between number of flowers and number of fruits. We measured on 10 different sites, several seasons. I would like to test if there is a significant difference in RS between sites. An example of my dataset:

I used Fisher's exact test - the same approach as in this example here: Fisher's exact test in R - 2x4 table - as follows:

> data <- matrix (c(6, 148, 0, 3, 0, 1, 0, 4, 2, 8, 0, 17, 8, 151, 11, 108, 1, 33, 0, 2), nrow = 10, byrow = T)
> row.names(data) <- c("1","2","3","4","5","6","7","8","9","10")
> colnames(data) <- c("fruit YES", "fruit NO")
> data
fruit YES fruit NO
1          6      148
2          0        3
3          0        1
4          0        4
5          2        8
6          0       17
7          8      151
8         11      108
9          1       33
10         0        2
> fisher.test(data)

Fisher's Exact Test for Count Data

data:  data
p-value = 0.3329
alternative hypothesis: two.sided


The result shows that there is no significant difference between sites, but if you check site no. 5 in the data, the percentage of fruit is much higher than the rest. Did I use the right test? If I did - did I do it right? Would you suggest any other method? Additional question: I would also like to check if the number of flowers and pH affect the production of fruits on each site. Which test/method should I use in this case - logistic regression? I'm very new to R, so a more detailed explanation would be very very appreciated. Thank you in advance!