Getting over 10k crowns in Arcade with 100 mist energy
Is it really possible to do that? Yeah who am I kidding ._. I just need crystal energy that's all and I do not wanna pay for Crystal Energy. I just need about 1k ce and that's it, but I'm not forcing a random Knight to give me it, I'll just get more and more crowns until I have 1,000,000crowns the person who gives me that 1k ce gets the 1m crowns. I'll inform you when I have that 1m crowns!
See ya in Haven!
Knight: Kitty-Max

Buy it in the market or it's too bad that you don't want to buy it. Your just paying more crowns for CE. It's like you want to pay 100k for each 100 CE. Just buy it at the market. It's cheaper than your deal.
Even people with elevator passes get up to 500k a month or so...

you can make more than 10k if you find the right recipes from Basil and resell them.
or do the fsc gate and maybe some arenas/danger rooms beforehand.

Running FSC costs you 50 energy and earns you at least 10,000 crowns (including the Almirian Seals). So you can earn 20,000 crowns using 100 energy.
If by "Arcade" you mean "not counting missions", then either use friends to get you to FSC (not easy these days) or sell recipes as Flowchart recommended.
There's no need to inform us when you get 1,000,000 crowns, but good luck.

T3 Arcade + FSC can yield more than 10k, plus profit from basil's recipe.
And I think the OP means that if you give him 1k ce now, he'll give you 1 mil cr in an undetermined future..

That's 7k x 2 = 14k. Hard part is getting to the terminal without using mist.

I've been dormant for awhile, but when I used to play regularly, Arenas and Danger Rooms (esp. in 2nd halves of tiers) were considered profitable and I think they still are even at today's CE prices. Graveyards also, if you're good at surviving them. I can't remember the average crowns different levels yield anymore (and it may have changed), but I'd expect arena-heavy T3s would be fine... still, since I've gotten back I haven't seen one person mention arenas when these profit questions are asked, so maybe I'm missing something.

Well, if you want to explore Clockworks the good old (and profitable) way, here are some tips on what maps to do (and not to do). I'm not sure if that would yield you over 10k per 100 mist though.
DO NOT's:
Treasure Vault (don't let the name fools you!), Concrete Jungle, Dark City, Briar Bone Barrage, Stygian Steeds, Candlestick Keep, Wolver Den, Devilish Drudgery, Scarlet Fortress (all except Grim Gallery)
DO's:
Battle Arena (always do all 3 arenas), Graveyard (easy money, watch out for red skeleton), Scarlet Fortress (Grim Gallery)
Maybe's:
Lichenous Lair, Aurora Isles, Jigsaw Valley, Starlight Cradle, Clockwork Tunnels, Deconstruction Zone
Also take into consideration the time you need to wait for maps to rotate. Time is money after all.

Scam
Not trying to offend you but how do we know this aint a scam someone will give you 1k ce and then you will suddenly switch haven and scam someone derp.
GL with getting 1million cr
BL with getting someone to give you 1k ce for 1million cr
Take the other guys opinions..... Buy ce (100 ce) 9.1-10 k each.

Because after gate rotation, people can look at the map composition and decide what gates they should do for the week. Determining which gates are most profitable (and rushing to the profitable maps) used to be part of the fun.
Mission systems, while interesting, take away some of these fun.
And needless to say you can always make all the stratum leading to FSC terminal with Fire or Shock fiends... That's part of the fun (?) too.

There was a gate that had three arenas in a row. It was glorious. You could get 8k from three depths. Achieving 10k+ was easy.

something smells fishy.
someone gives you 1,000 ce and you make 1 million crowns and give away the 1mil crowns?
for me this is a scam.
Me and my guild mates did Arcade runs from depth 1-29 after a few days we've gotten over 1,573,058cr and nevermind, I've gotten enough energy to go from depth 1-29, I was doing that for fun, sorry guys ^^;
1mil for 1k CE...
Thats a bit of a bad idea.