How EOS is different than Ethereum that it brings block time to 0.5 seconds?
In EOS, each producer creates 6 consecutive blocks before handing off to the next producer. Therefore, in these 3 seconds (6 x 0.5), there is no latency to propagate blocks as they're created by the same producer. The latency is a problem during hand-off, so it's possible that the last few blocks or the next few blocks get orphaned, which is why there are plugins suggested to minimise latency by accounting for geographical location of BPs.
And why 21 and not for example 1001.
I answered this on the EOSIO StackExchange, so I'll paste my answer here:
It's a number that Dan Larimer arrived to after some experimentation in his previous projects (BitShares, Graphene, and Steem.) For instance, one of Dan Larimer's previous project, BitShares had 101 producers, and he mentioned that this raised a significant governance issue as members of the community wouldn't keep up with researching 101 different BPs and educate themselves to vote accordingly. Therefore, based on user feedback, he decided on a number that would allow people to stay informed while also providing security via block producing decentralization.
For Dan Larimer's explanation, see this video interview. Excerpt:
I introduced first version of DPoS with 101 block producers. They were all elected by approval voting, and then BitShares 2--or Graphene--reduced the number from 101 to a user-defined number so that as people vote they can vote... if they vote for more, then there will be more; if they vote for less, there will be less, and that gives you an idea of how many people the community is actually able to vote for and what we saw was that when the community is in control the quantity it stayed around 15 people or so.
So with Steem, I made the decision to just hard code it to 21, which would be more decentralized than the community was doing on its own and BitShares because that was about the throughput of the attention and the ability of people to vote.
What are the things that EOS can do that Ethereum cannot?
Ethereum vs EOS: Technical Differences.
Ethereum vs EOS: Scalability.
These are very broad questions difficult to answer here. I suggest taking a look at the whitepaper as it may answer your questions.