I have my Grandfather's Ithaca, which I always thought was a Flues model, but I now think it is an NID (New Industry Double) but I am not certain, and not an expert, by any means. That gun has completely different engraving from yours, mine has the dog (pointer?) on the receiver. My gun was made in 1909, that is verified fact. My Grandfathers gun has "fluid steel" barrels, making it safe for modern smokeless shells (of moderate power)
Don't know if your Flues model does, or not, sorry. It doesn't look like twist barrels, but you need a expert's opinion to be sure its safe to shoot.
USUALLY the right barrel is more open choked than the left, but any combination is possible, as Ithaca would make what ever the customer wanted.
My Grandfather's double has 26" barrels, and is choked FULL/FULL which is how he ordered it. Also has the stock made to his order, with a bit more drop than usual. makes that gun a real experience to shoot!
Sweet old Ithaca, in excellent shape! Congratulations!