Most likely, I'm not exactly sure how they keep track of the costumes but they do reply to the costumes entry with a thanks. Hopefully they accept what you put in.
I hope so too. Its now past 12 in the UK so technically I don't think I can enter again even if I wanted to. But since you confirmed you can see it I'm reassured that it at least processed ^^
You can check the times of the tweets (according to my timezone, you posted the design to the 15:46 and TN his message to the 16:18). So everything should be OK
I just checked my twitter setting and it was set to GMT +1 hr OMG! So it said 12.46am O_O. I changed it to London time which was 11.46pm which is where I'm from so I hope everything is ok!