Translation:Those shoes are orange.
It's not the same. Ano is modifying kutsu, this means it goes with shoes, it clarifies which shoes the speaker is talking about. Which shoes? Those shoes. If you wanted to say Those are orange shoes then you would say - are wa orenji na kutsu desu - those (things) are orange shoes. In the latter example you can see that orenji, the colour, modifies/describes the noun - not ano.
オレンジ can refer to the color of the fruit. but when refering to the color both オレンジ and オレンジ色 is fine. just いろ clarifies its the color.
I looked this up in my jisho and it had it listed as "a bitter orange" and the colour orange with iro on the end. I have never heard of it or heard it used though. The anglicised orenji must have superseded it. orenji was in common use already by the late 80s but I couldn't tell you how long it has been in use.
In Japanese, closed vowels ('u' and 'i') tend to be hushed or wispered if they come in between two voiceless consonants or at the end of a word/sentence after a voiceless consonant. That's why certain names in anime seem to make those vowels silent. You know Sasuke from Naruto? Everyone pronounces his name like "sahs-kay", on account of the 'u' coming in between an 's' and 'k'. If either of those voiceless consonants were replaced with their voiced counterparts, (i.e. giving "sazukei" or "sasugei") that 'u' would be every bit as loud as the other vowels.
EDIT: This rule applies to all words and phrases by the way, not just nouns. The verb endings "~masu" and "~mashita" come to mind, as they are pronounced closer to "~mas' " and "~mash-ta" respectively.