Get type of all variables

You need to use get to obtain the value rather than the character name of the object as returned by ls:

x <- 1L
typeof(ls())
[1] "character"
typeof(get(ls()))
[1] "integer"

Alternatively, for the problem as presented you might want to use eapply:

eapply(.GlobalEnv,typeof)
$x
[1] "integer"

$a
[1] "double"

$b
[1] "character"

$c
[1] "list"