Do web wallets keep customer accounts isolated? Say there's an online wallet or exchange or some site, and they give me an address to send my bitcoins to.

I get the public address but not the private address because technically those bitcoins are now "theirs" - and i'll use them to exchange for other crypto currencies at some time.

But the public address is listed on sites like blockchain.info and I can see all of my transactions to that wallet.

Is it normal to see transactions going out of that wallet, even if I haven't spent those bitcoins with the service? Is my wallet isolated to transactions I might conduct?

Or do they use a normal bitcoin server, so whenever anyone withdraws, it uses whichever bitcoin transactions are available in this company's entire collection based on their bitcoin servers algorithms using all the accounts listed?

In theory, it shouldn't matter, so long as the total amount in everyone's accounts is equal to the total amount in all of the private keys they maintain. But do any of the services keep them isolated as sort of a check to make sure that a customer's coins are still there and it's not some type of ponzi scheme?
There are different kinds of web wallets. Some are more like pieces of software that you re-download every visit, but you still actually own the private keys (re-downloading is still a risk, mind you). But in this case it looks like you're talking about an exchange or other web wallet where you don't actually own the coins anymore (i.e. they have the private key). Yes, in that case it's normal that coins are not isolated anymore. And yes, that is extremely dangerous and has gone wrong many times before.

In general try to avoid web wallets and if you really need to use for example an exchange, try to move out the Bitcoins as soon as you can, to minimize your exposure to this risk. If you're actually actively trading on such an exchange, then you don't really have a choice and simply have to accept the risk of losing all your coins one day.