Writing personal translation app using my own database to work on android
Android studio covers basically every aspect you've mentioned. You'll probably need to google a lot to learn how to implement individual things.
Short guide: (research on your own how to do each step)

You can use SQLite database for storing your data.
Add your media (sound files) to resources and then play them or whatever
Android keyboard supports different languages, just set it to Romanian

You will need some basic understanding of Android programming if you want to do this. I'm uncertain how much time you're willing to put into this, but it should be doable in 2-3 weeks, heavily depending on your previous coding experience.
I would like to make an app that lets you search for part of a word or phrase, then returns the closest results from a personal database of words I have learnt in another language. Once the results have been returned I would like the option to play the sound file with the associated results. I can write the database in whatever program I need, and the sounds files would be in either wav or mp3 format. The app would also need to allow the user to input foreign letters, there are about 10 extra required as I am using Romanian. These could be separate on the screen if necessary, as in separate to the keyboard input. 
Would this be an easy enough project to undertake, what sort of size would it be, I am more than happy to spend about a week on it. I am familiar with coding, particularly in Python, so writing in Python would be best, but I can use Java also. This would need to work on the android system. What is the best program to use to write the app?