The miner software computes hashes at a lower difficulty than required for a block. This is probably what your seeing. If you were pool mining, these would be shares.
No, solo mining does not have that concept at all. There's one difficulty and one difficulty only - the one that matters to make it into the block chain.
pyrohydrosmok, mined blocks do not show up in your wallet until they are buried under 100 other blocks. That's to prevent them being spent in case the block chain splits, and your block ends up NOT being the one chosen by the network for the chain. Give it another 13 hours or so, and then it should appear in your wallet.