What are the differences between concatenating strings with cat() and paste()?

What are the differences between concatenating strings with cat and paste?

In particular, I have the following questions.

1. Why does R not use the double quote (") when it prints the results of calling cat (but it uses quotes when using paste)?

   > cat("test")
   test
   > paste("test")
   [1] "test"
   

2. Why do the functions length and mode, which are functions available for almost all objects in R, not "work" on cat?

   > length(cat("test"))
   test[1] 0
   > mode(cat("test"))
   test[1] "NULL"
   

3. Why do C-style escape sequences work with cat, but not with paste?

   > cat("1)Line1\n 2)Line2\n 3)Line3")
   1)Line1
    2)Line2
    3)Line3
   > paste("1)Line1\n 2)Line2\n 3)Line3")
   [1] "1)Line1\n 2)Line2\n 3)Line3"
   

4. Why doesn't R's recycling rule work with cat?

   > cat("Grade", c(2, 3, 4, 5))
   Grade 2 3 4 5
   > paste("Grade", c(2, 3, 4, 5))
   [1] "Grade 2" "Grade 3" "Grade 4" "Grade 5"