PoS coins use 10% of stake and dropping as economic activity goes up.

Which PoS coins? I'm aware of only NXT, which has much more online, but then it works in a different way. Peercoin isn't PoS, it failed, very bad design.

 Let alone that their profits are tiny to justify such big stake in minting (Just early adopters minting to support their system). If a real economy exists many will put their coins in more productive uses than minting and will not even care.

Coins aren't productive, they can be either online or offline, that's it. Online forges.  

Why do you assume all these nodes will be online at the time of the attack?
I didn't wrote that. Still, even at your 10% of honest stake, as you said, you need >10% of hostile stake. That's still much more as % of market cap

Why do you assume that lending will be something everybody will do? Why do you assume that it will not backfire giving one person extreme stake history who might not care about the coin at the present?
Not everybody, just people with small amounts. First, it's not like there's only going to be one person. Second, big holders will dominate with their own nodes. Third, doing an attack like this would be actually criminal, so don't lend forging power to anonymous people in third world countries and it's going to be ok

Why do you say lend your coins to a person you can trust if you want to build a trustless system?
Not lend coins, lend forging power. It's not required, but it makes the network a tiny bit safer

What about the fact that coins get lost and later stakers will have less cummulative total stake available?

It's true that it's a problem if the loss amount is extreme. However, over long periods the validity of older blocks will be close to 100%, as many different stakes will get transacted.  

Why do you assume that the rest honest stakers (those not having their coins reversed) will not mint both chains?
As gmaxwell said a rational miner will mine both chains to maximize profit.

It's trivial to create a rule which makes one block with identical stake better than another, like a comparison with hashes. This would lead the honest nodes to completely ignore the worse block. To break that would be equivalent to acting directly against self financial interest, for no reason, and as long as all people in control of a currency don't act against their interests, everything works.  
It's no different to PoW. If I own serious money in a specific cryptocurrency, I'm not going to endanger that, because that would be very costly, although indirectly, just as mining forks in PoW is costly.

Most people living in skyscrapers don't steal and destroy bricks from foundation.  

Note that it takes just one person with one coin to behave correctly, even if literally everyone else is signing all forks, and everything works.  

Why for no reason? Because this shouldn't be profitable, if it is, it's a design error. I don't think it's that important though.  

All PoS coins are very centralized in their stake distribution and dont forget that when you say they are decentralized. Let alone all the other reasons PoS coins are not decentralized.