Plotting multi-dimensions of data using ggplot2

I have below mentioned directory structure:

Folder named A contains txt files named 1, 2, 3, .., 5
Folder named B contains txt files named 1, 2, 3, .., 5
|
--A (Folder)
  |---1.txt
  |---2.txt
  ....
  |---5.txt

--B (Folder)
  |---1.txt
  |---2.txt
  ....
  |---5.txt

I am reading these text files into data frames through 2 nested for loops. Single data frame looks like this:

df <- data.frame(Comp.1 = c(0.3, -0.2, -1, NA, 1),
         Comp.2 = c(-0.4, -0.1, NA, 0, 0.6),
         Comp.3 = c(0.2, NA, -0.4, 0.3, NA))
row.names(df) <- c("Param1", "Param2", "Param3", "Param4", "Param5")

Values always lie between -1 and +1. Number of rows (parameters) and number of columns (components) of all these data frames are not same. For eg: the above data frame is of 3x5, others can be 5x15, 4x10, 5x40, etc.

I want a plot that has:

1. parameters on x-axis
2. components on y-axis
3. values as points in the above graph 
4. shape of point representing folder name (A = square, B = triangle, C = circle, .., E)
5. color inside the point shape representing file name (1, 2, 3, .., 5)
6. color intensity describing value (For eg: light red [almost white] color representing closer to -1 like -0.98, dark red representing closer to 1 like 0.98)

I have this code:

alphabets = c("A", "B", "C", "D", "E", "F")
numbers = c(1, 2, 3, 4, 5)

pca.plot <- ggplot(data = NULL, aes(xlab="Principal Components",ylab="Parameters"))

for (alphabet in alphabets){
   for(number in numbers){

   filename=paste("/filepath/",alphabet,"/",number,".txt", sep="")

   df <- read.table(filename)

   #Making all row dimensions = 62. Adding rows with NAs
   if(length(row.names.data.frame(df))<62){
      row_length = length(row.names.data.frame(df))
      for(i in row_length:61){
          new_row = c(NA, NA, NA, NA, NA, NA)
          df<-rbind(df, new_row)  
      }
   }

   df$row.names<-rownames(df)
   long.df<-melt(df,id=c("row.names"), na.rm = TRUE)
   pca.plot<-pca.plot+geom_point(data=long.df,aes(x=variable,y=row.names, shape = number, color=alphabet, size = value))
   }
}

Output of this code is this:

EDIT: After following @Gregor's steps mentioned in comments, I have a big_data_frame like this: head(big_data, 3)

Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 params alphabet number 1 NA NA NA NA NA param1 A 1 2 NA NA NA 0.89 NA param2 A 1 3 NA -0.95 NA NA NA param3 A 1