[Ethereum] How many nodes are there on the Ethereum network

The answer is here on the Ethereum wiki. It's too long to quote here. One thing to note is that when you want the value of the WS_SECRET you click on the link and it opens up Skype (if you have it installed and associated with the skype: protocol) and the value you want is in the name of the channel - you don't need to ask anyone on Skype.

Another tip is that if you drop off the page, it may be because the server's been rebooted, in which case you need to restart the stats process as described on the wiki page.

I think that Bitcoin wiki has a good article: https://en.bitcoin.it/wiki/Full_node its not for ethereum but the concept is pretty much the same.

Full node is somebody connected to p2p network that verifies the blocks. I believe that all ethereum clients at this point are full nodes.

Lightweight nodes do not check or download the whole block-chain. See this: https://github.com/ethereum/wiki/wiki/Light-client-protocol

Miners are full nodes that, in addition, validate the new blocks by solving a crypto problem.