Do you need to worry about IP issues with respect to people testing your service and giving you suggestions? They might be doing so while at work for example.

No. And please don't use "Intellectual Property" generically unless you know what you're doing.

Trademarks have nothing to do with your question.

Copyrights have nothing to do with your question.

Patents are always a risk, but you're no more or less liable by knowing it was someone else's idea. You're only more liable if you know somebody else got a patent.

If the testing and suggestions are extensive, their employer might argue that they have some claim to the IP for your startup.

An interesting issue but I've never seen any reference to this kind of problem. I personally wouldn't worry about it. As already pointed out trademarks/copyrights are unrelated and also patents are for specific implementations of ideas -- they don't cover broad concepts.

Not if you don't credit them as part of the development. If I worked for BigCo.A and sent in customer feedback to SmallCo.B's new web startup, A has no claim in IP. If I'm just leaking inside info from A to B, that's another set of issues altogether.