Is google translate monolingual definitions open for commercial use? Am I violating intellectual property to use english words definitions in my english quiz app?
If you are using the Google Translate API then you are allowed commercial use. But there is no free quota for the API (terms of service, pricing). If you are a paying customer, you can use the translations for commercial use (with attribution if you use them directly).
I suspect you are not talking about the paid API but instead either scraping yourself or using a package like goslate. These tools are against the Terms of Google so you may find that they aren't very stable (goslate works by faking a user-agent). Building a commercial app based on these data sources is probably not a good idea. See the comments here for more discussion.
(if you want simple, single word translations with a flexible license, check out using Anki decks, for example)
The official Google Translate API does not offer dictionary data. (If you must know: Google has traditionally paid for licences for dictionary data from various sources, with varying quality, for the various languages.) So I assume you are scraping and thus on poor legal footing, but I doubt it will be a problem in practice.
One great and ever-improving source of dictionary data is Wiktionary. There are well-tested open-source parsers and clients available, just like for Wikipedia.