which web of trust exactly are you talking about, that pools should be part of?

i only know about the #bitcoin-otc (which is an irc-channel-marketplace) web of trust,
but that has nothing todo with nodes, or miners, or pools,
it's just individual users that buy and sell bitcoins, or goods or services for bitcoins.

oh, i see.

well, yes, pools are a single node (depending on the pools setup maybe 2, or 3 nodes).

workers, the mining-clients that are connected to the pool, are no nodes at all,
they are just some kind of bruteforcing tool that's hashing some data sent to them by the pool-server.
those workers themselves are in no way connected to the bitcoin-network, they are only connected to the pool-server.
the pool-server then is connected to one, or more bitcoin-nodes.

from a security point of view, pools nodes aren't any different from other nodes,
everyone is treated equally, they either follow the bitcoin-protocol-rules and everythings fine,
or they create their own rules and so create their own network, because everyone else will just ignore them.

of course its influence on the bitcoin-network IS proportional to its hashing power.

mining-nodes have influence, non-mining-nodes only participate without any influence.

every node verifies blocks that it gets from other nodes, to check if they are valid,
blocks contain hashes (from the previous blocks and transactions), that everyone knows about (because it's written in the blockchain), but non-mining nodes don't need much hashing-power to verify blocks (smartphones work well).
non-mining nodes just don't create any new blocks, they download them as soon as someone else creates them
and you only have influence, if you create new blocks.

Yes, that is true. There has been a few discussions going on about the size of Tycho's pool regarding this topic.