Question: Let's say for example I put my public bitcoin address on a website for donations and multiple people for around the world deposit bitcoins simultaneously to that same wallet: 

1. Will all deposit transactions be valid on the bitcoin network or might some transactions "overwrite" the other?
2. While receiving bitcoins from someone (not yet a verified transaction on the network), can I withdraw or pay bitcoins using the same wallet given the amount only include previous bitcoins and does include the new deposit?

Answer: 
One big reason against this sort of thing is that it creates a huge incentive for bad people to try to prevent you to do transactions (censor you). 

1. If miners get the "lost" bitcoins they might simply refuse transactions with coins that are almost expired hoping to get a bigger reward later.
2. If miners don't get them but they are truly lost forever, then there is an incentive for big stakeholders to try to do the same thing: less coins means the value of everyone else's coins goes up.
3. It gives governments and other mafia huge power: don't want to comply? We'll just lock you up for 2 years and make your coins expire. Or more "humanely" use other censorship tricks (hacking/digital censoring) to prevent you from spending your coins before they expire.

Another reason is that people will en mass set up automated scripts to move all their coins regularly, which is a big security (and privacy) risk. It's much easier to keep private keys safe (on a piece of paper in a vault) than it is to keep an internet connected system powered up and safe 24/7.
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> Recycle lost/destroyed bitcoins by giving them back to miners
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> Miners will continue to get more transactions and thus more fees
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If you already own bitcoin, this isn't a good thing as it increases the supply. That said, there is an altcoin called [Freicoin](http://freico.in/) that uses demurrage rather than an abrupt 2-year expiration that's got some of the property you're looking for.

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> Number of unspend transactions may become less speeding up verification
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> Size of blockchain to keep downloaded can be minimized
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This may or may not be true as expiring coins gives people incentive to transfer them in order to not lose them. I would guess that given this fairly major economic incentive, the number of unspent transactions wouldn't actually go down that much.

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> Broken cryptographic hahes/signatures can be made obsolute
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> New features can be easily introduced
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You seem to be of the opinion that what's keeping bitcoin from innovating is that there's all these obsolete transactions. That's simply not true. What's keeping bitcoin from innovating is the possibility of a hard fork. New features like lifting the 1MB block limit has nothing to do with old transactions being in the blockchain. It has everything to do with miners achieving concensus.