How to run multiple commands at once.
Try putting this command macro into a Tool Palette button:
^C^CExplode ALL -Overkill all ;;SELECT \Pedit m P ;j ;c ;-Purge a * n;
Some things needed tweaking [e.g. the hyphen prefixes on some command names, spelling out of ALL for the Explode selection, the * for all in the PURGE command] compared to the literal aspects of your description, so I hope it ends up doing what you need.
The SELECT command with one backslash for user input can take any amount of selections and selection options [unlike other commands involving object selection that would need separate User-input backslashes for each selection], then the PEDIT command uses the Previous selection established by that. Spaces are just like spaces or enters at the command line; semicolons are Enters. [Many people like to use semicolons for all; I prefer spaces except when there is more than one together, in which case with all spaces it's harder to "read" how many there are.] The ^C^C at the front is a double cancel, to ensure you get out of any command that may be running when you pick the macro.
Note that the (initcommandversion) business described by @cadffm is needed only if you do the Exploding in an AutoLisp (command) function, which can Explode only one thing at a time unless you do that or use other ways to handle that limitation. It is not needed in a direct command-line Explode command such as in a macro.
[You can shorten it by one character if you set the PEDITACCEPT System Variable to not ask whether you want to convert Lines and Arcs.]
