Is custom skins allowed

yes as long as they aren't just a complete copy of existing skins

To elaborate on what UnboundHades is saying, custom skins that aren't custom and are just stealing from Riot are definitely not allowed, but otherwise skins that do not provide a measurable advantage to the player (like giving easy to see hit box indicators) are typically ok; what you want to watch out for, though, is if the program you are using to swap the skin out is allowed. The use of any 3rd party application is done at your own risk (Riot isn't responsible for it breaking your client or giving you a keylogger or virus), and if the application has any feature that is against the rules (like a dodge script) then the whole thing is off limits.

For more info on 3rd party app use, check these posts;

http://boards.na.leagueoflegends.com/en/c/player-behavior-moderation/5dmkJinG-3rd-party-applicationsmodifications-whats-allowed-and-what-isnt

http://boards.na.leagueoflegends.com/en/c/miscellaneous/5kx4F7VE-reminder-third-party-applications

Yes, but its a bit dodgy and understand a lot of custom skin programs contain scripts which you will be banned for even if you don't use them.

If you want to use custom skins I would recommend using the program Wooxy and probably map skins, I've used it in the past and never had any problems with it

I used to use Wooxy but with the ban waves for 3rd party programs I got a bit too nervous and stopped. It's a bit risky since your sort of dancing in the gray area.