list all functions on CRAN

You can use the sos package, for example:

library(sos)
findFn("adply")

The output is an html including links to online documentation packages.

collidr package will give you this

library(collidr)
collidr::CRAN_packages_and_functions()

It will return a list of packages and their functions from CRAN i.e.

#          package_names                function_names
# 1                   A3                    A3-package
# 2                   A3                            a3
# 3                   A3                       a3.base
# 4                   A3                a3.gen.default
# 5                   A3                         a3.lm
# 6                   A3                         a3.r2
# 7                   A3                       housing
# 8                   A3            multifunctionality
# 9                   A3                       plot.A3
# 10                  A3               plotPredictions
#    ...             ...                           ...
# 294181            ZVCV                          getX
# 294182            ZVCV              helper_functions
# 294183            ZVCV                           VDP
# 294184            ZVCV                          zvcv
# 294185            ZVCV                  ZVCV_package
# 294186             zyp                   confint.zyp
# 294187             zyp                           zyp
# 294188             zyp                       zyp.sen
# 294189             zyp                 zyp.trend.csv
# 294190             zyp              zyp.trend.vector