Use the repeat command (C-x z) to repeat the last
command. If you preface it with a prefix argument, the prefix arg is
applied to the command.
You can also type C-x ESC ESC
(repeat-complex-command) to reinvoke commands that used the
minibuffer to get arguments. In repeat-complex-command you can
type M-p and M-n (and also up-arrow and down-arrow, if your
keyboard has these keys) to scan through all the different complex
commands you’ve typed.
To repeat a set of commands, use keyboard macros. Use C-x ( and C-x ) to make a keyboard macro that invokes the command and then type C-x e. See Keyboard Macros in The GNU Emacs Manual.
If you’re really desperate for the . command in vi that
redoes the last insertion/deletion, use VIPER, a vi emulation
mode which comes with Emacs, and which appears to support it.