Hey, I can answer this! Cool!

Something is different about server2. Really, it is. It may not be worth looking for, but there is something.

There is a cool expect feature to cut out the prompt, actually it's more of the entire purpose of expect than a feature.

Re the no-key problem, again this is what expect is great for. It can compare input to a list of patterns, so if it gets a "password: " instead of a command line, it can do whatever you want. You're also not limited to whole lines or lines ending with a newline, so it won't have trouble because the cursor is sitting there on the same line as the "password: " prompt.

Re the waitfor, yup you got it. The whole thing is in the stdin. As long as a previous expect statement hasn't cleared out the buffer, you're fine.

You may want to step back and play with expect by itself and then apply it to SSH, rather than making SSH work before moving on to expect. Expect takes a little work to wrap one's head around, so it might be worth while to do that in a simplified environment.