The course list in the iOS app is ordered by recency, so the one you most recently learnt or reviewed words in will be at the top. You cannot change the order of your courses at the moment.
You can Quit a course by tapping on the trash icon in the course options. Please note that this will remove the course from the list, but it will not delete your progress.
The app will prompt you to Learn New Words or Review the ones you have already learnt. Alternatively, you can choose which session to start from the mode selector screen (to open it, simply tap on the four coloured dots).
To find out more about all Memrise learning modes (free and Pro), see Memrise Pro in the iOS app.
If you would like to skip an item, click on Skip and you will be taken to the next word/sentence.
The elements in grey give you additional information about the item. They are called attributes: you will not be tested on them, but they add information you may find useful (e.g., to disambiguate between nouns and verbs).