I'll try to answer what I can:
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You either have to run a node or trust somebody else (like MyBitcoin.com) to keep a wallet for you.
Your account balance is stored in a Berkeley DB file called 'wallet.dat' (what directory depends on your operating system; on my Mac it is ~/Library/Application Support/Bitcoin/wallet.dat, on linux it is ~/.bitcoin/wallet.dat, not sure about PCs).
The only application that can read wallet.dat is the bitcoin code, and the database structure isn't documented anywhere besides the bitcoin C++ source code.
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Theoretically, no, but the code to do lightweight validation hasn't been written.
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Satoshi is planning on encrypting the wallet database, so you'd need to enter a password to read it. (and they need to get your private keys to generate transactions-- those are what are stored in the wallet.dat)
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Dunno.
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There's another thread about this in these forums; maybe we should start a "Satoshi's TODO list" thread and get folks to volunteer to help out.
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Fewer and fewer coins will be created over the next N years (where N is-- what, 20?). That's a feature, not a bug...
RE: developing your own version: are you thinking of creating a second bitcoin implementation that is compatible with the existing C++ one (good idea, in my opinion)? Or creating a similar-but-not-the-same system (bad idea, in my opinion)?