How does Eligius pay miners directly from the newly generated coins?
It simply generates the coinbase transaction to include payments directly to its miners, instead of only a transaction to itself.
What are the pros and cons of this compared to how Slush does it?
Here are some I can think of:
No transaction fees necessary for these payouts (...
By simply adding addnode=184.108.40.206 to your bitcoin.conf file then any transaction you send will automatically be broadcast and eventually make it into a block. No one but you has to add this node and nothing special needs to be done beyond this one configuration.
Now it may be true that the bitcoin-qt client will not actually allow you to send a ...
Do you want to create p2pkh output and send zero satoshies on it? Such output is non-standard (dust) and will not be relayed and mined (but it is possible)
Or may be you want to create nulldummy (OP_RETURN) output? This is possible
BTW, sometimes miners confirm non-standard transactions, for example https://blockchain.info/tx/...
In the last few hours I am getting 100% connection rejections from
Eligius. I am using a Mac and the Asteroid miner GUI. I also have
MacMiner setup. both are not failing after about a month of
successfully working. But that is not the point of the question.
Check your ISP, check luke's threads on btctalk and on eligius or their IRC chan #Eligius on ...
For the second part of your question:
Some EWallets can handle generated bitcoins, some can't -- depending on what client they are using. If the wallet refuses to support these, you could losse funds. i.e., it is best to not use an EWallet when mining on Eligius, P2Pool or any other pool that generates coins directly to the address supplied by the miner.