No, your shadow has no feelings.
Rouge has friendly/business relations with Shadow and nothing more. Shadow does not test any feelings to Rouge and she knows it. Although she does have a slight attraction to him, but shadow doesn't return the favour
No.
Technically, Shadow can love anyone, but he simply chooses not to express his feelings for any of the Sonic characters. In fact, Shadow is very restrictive and chooses to keep a tight lid on almost all of his emotions.
Shadow shows no romantic feelings towards anyone.
As of yet, Rouge has not been stated to have feelings for any character with the exception of her crush on Knuckles.
There is no website that shows that Shadow likes Amy. Shadow has no feelings for Amy what so ever. Amy has no feelings for him eather, She only likes Sonic. When Amy hugged Shadow it ment nothing, She only hugged him thinking he was Sonic not because she liked him.
He cares for her too, but not in a way that he has feelings for her.
Aside from brotherly love to Maria, no. Shadow displays no romantic feelings for anyone at this point.
He might have had feelings for Maria, but it is not known.
Adrian flirts with Rose in Shadow Kissed and makes his feelings clear to her near the end
well they do have feelings but not particularly but the have asked each other out and they did but then... sonic steps in to it and then gets sally.............. and Amy steps in and gets shadow THE END
No he never has, probably never will, and neither will any character in the Sonic series as there are no canon couples and will probably remain that way.