The data you have is what we call wide data. The names of the Observation stations are in the columns. It would be easier to calculate what you want if you have the names of the observations as another column. You can convert from wide to long using the tidyr::pivot_longer() function as shown below.
myData <- myData %>%
tidyr::pivot_longer(cols = -(c(fetcha, hora)), names_to = "Site", values_to = "Value")
and then create the Month column to aggregate using lubridate::month() and then group by Month, Site and summarise by mean(Value)
monthly_averages <- myData %>% mutate(Month = lubridate::month(fetcha)) %>%
group_by(Month, Site) %>%
summarise(Monthly_Avg = mean(Value, na.rm = TRUE))
# the na.rm argument ignores the NA values while calculating the averages
You can then convert it back to wide format using the tidyr::pivot_wider() function.
monthly_averages %>% tidyr::pivot_wider(names_from = Site, values_from = Monthly_Avg)