Q: Is it possible to download Wiktionary?
A: Yes. https://dumps.wikimedia.org/enwiktionary/ should have the latest copy of the main namespace. The cleanest navigation page is https://dumps.wikimedia.org/. Just download a -articles.xml.bz2 file and some software to read it (for nix, for Windows).
Q: Can I use data from Wiktionary in my program?
A: As long as you meet the conditions of the GNU Free Documentation License or Creative Commons Attribution/Share-Alike License, certainly.
Latest dump for English is from September 1. I wouldn’t know whether it has all the data or how easy it is to parse it.
Indeed, it depends on the language and your goals - I had a very high success rate plucking out Russian grammatical tables from English Wiktionary with a few hours of scripting the data cleaning (https://github.com/thombles/declensions). I have a theory that you could get better results using an offline archive of the page sources but haven't tried this yet.