Hi Madara. Welcome to the forums. To answer your questions,:
1) When a Bitcoin client is loading blocks, it is loading a complete history of every transaction that has taken place over the Bitcoin network. When a "block" is successfully mined by a user, that block contains all of the transaction information that has taken place over the entire network since the last block was found. The 0.5 BTC you have made so far was carried on these blocks, and the entire network confirms that these 0.5 BTC indeed belong to you. Think of it as a way of proving that the transaction(s) took place. As for the amount of space taken up on your PC, you should have at least 3GB of hard drive space (not to be confused with RAM) free and dedicated to storing the block index. As of this writing, the block index is only 2.7GB large, but will get bigger as time goes on and more blocks are discovered by the network. When you open your wallet up again in the future, you will only need to load the blocks that have been discovered since the last time the wallet was up-to-date.
2) This question is hard for me to answer; I've never tried buying BTC directly with a debit card. Credit cards are a no-go because you could just charge-back the charge and reverse the transaction, so nobody will accept credit card payment for BTC. However, you can buy Second Life Linden with credit, and then sell those same Linden for BTC. As of this writing, Second Life Linden is the 3rd largest volume exchange for BTC.
3) Unfortunately mining with Processor power is no longer viable, so your dual-core won't do much good here. The nVidia 4500 GPU is not capable of OpenCL, and OpenCL is needed for mining with a GPU(even so, nVidia cards are no good for mining. You want ATI/AMD video card/GPU). As for the laptop, it's typically not a good idea to mine for BTC with laptops due to heat issues, even if they do have an ATI/AMD GPU in them. You don't want to overheat your laptop and have it permanently crash on you. A typical dual-core CPU will mine at roughly 2 megahash/s, which would yield all of... 0.000001 BTC every 24 hours? Rough estimation, but yeah, not worth it. You want to mine with a GPU/video card, or specialized mining equipment such as an FPGA or ASIC.
4) Other than the free bitcoin "faucets" which you have apparently already found, there is no way to get "free" bitcoins without mining them yourself, and I've covered mining with the 3rd answer above. However, there are ways to get Bitcoin by doing "work" over the internet;
www.bitcoinjobs.com ,
www.reddit.com/r/gonewild ... These sites offer to pay you in Bitcoin for jobs/services.
I hope these answers help! Enjoy, and good luck!