The most interesting part is that Iconomi keeps growing its funds due to the BTC rise and next week when LSK pumps it will go even higher. Fun times ahead on all fronts here

It would be interesting if they promised to pay dividends in USD.
Otherwise it all depends on BTC/ETH price, and the prices of other cryptos they (will) own.
No it doesn't. You can convert your ETH dividends to any currency, crypto or fiat immediately.
I don't see any problem here.
Yup, 1BTC worth of ETH is still 1BTC no matter the ETH price.