What happens if I start a new transaction with funds from a transaction which isn't 100% complete?
Let's say, the incoming transaction shows 2/3 of the green dot, but the sum is counted as full by my Bitcoin Wallet for Android.
The green dot in
Bitcoin Wallet for Android represents the number of confirmations an incoming transaction has. Once the first slice appears, the transaction has its first confirmation; i.e. it was included in the blockchain. Additional slices will appear when succeeding blocks are found, AFAIR marking up to six confirmations.
There should not be any issue or delay to spending any funds that have at least one confirmation as long as you include a sufficient transaction fee.
You transaction will remain unconfirmed until all the inputs to your transaction are confirmed. Assuming proper transaction fees were paid for the unconfirmed payment you are waiting on they will confirm. Once that happens your outgoing transaction will confirm as well.
Your wallet will always search for confirmed inputs first and only uses unconfirmed inputs as the last resort.
To avoid creating chains of confirmed transactions always include an appropriate transaction fee.