I created a wallet in blockchain.info android app. I bought 0.2830 BTC onto my new address. Then I made another address, tried to send 0.0001 BTC to that address (without a fee / 0 fee). Now it stays unconfirmed as you guessed. I just wanted to kind of test sending btc between addresses.
The problem is I want to send larger payments with a fee to another address but blockchain.info android client says "No free outputs to send". Why is it that if I have one unconfirmed transaction all of my btc address balance becomes unusable?
Because you only have the single input to spend. Think off it like you received a 0.2830 BTC bill and now you try to spend 0.0001. You have to use the entire 0.2830 BTC bill for that. Once the transaction is confirmed you will be able to use the change.
I have now spent multiple hours reading and searching the internet for some quick solutions to this problem. But as I am relatively new to bitcoins (although I have IT and Computer Science background) I have not found a step by step guide.
There is no quick solution, there is no easy solution either, besides waiting. You can either try to export the private key from your wallet into another wallet and try to double spend the transaction or wait. Regarding the time you have to wait, it depends, but the rule of thumb would be 1 bitcoin needs to wait 1 day to go through without a fee, you try to spend 1/10,000 of that, thus the prediction is that you have to wait 10,000 days. Keep in mind that its a rough estimate and you might only take a week or month etc.
I read that it may be possible to export my wallet from blockchain.info app to another wallet and try to send all of my account balance to some new address, which would invalidate the unconfirmed 0.0001 transaction, but as I have not found a step by step guide I do not feel confident doing that.
Nothing you can do will invalidate the transaction you created, you can only hope that the network forgets about your transaction.
This indicates that most of the network forgot about your first transaction. Thus once bitcoin core is synced you should be able to double spend your TX.