Since you are pretty new to the wrench turning business, my suggestion is that you take the carburetor off and take it to Autozone and exchange it for a rebuilt 2100. Although not real sensitive, the carburetors can be a PIA if you are not used to dialing them in.

 

Remi - welcome to the forum and nice car ! concerning the carburetor issue, I think you should follow the recommendation from Soaring, excepted if you spot very easily a reason for the choke plate not to move ... if you could upload some pictures it would be great!

For the oil leak, get undet the engine and try to the see where it is coming from ... it could be the gasket of the oil pan where it interfaces with the engine, or it could be the gasket at the bolt at the bottom of the oil pan ... or it could be somewhere else ... if you cannot locate the origin of the leak, than go the mechanica

Some additional questions - the car looks really good, but did you get it inspected prior to buying it? do you know how much work has been done on the engine ... some more pictures of the engine compartment and interior would be great as well

Merci et bonne chance!