Search Bar and TOS again

I know it is against the TOS to change the code of Google search bar etc.
But is this page [removed] against the TOS?

They modified the input field with a related keyword and also said something like "not satisfied? try google?"

Am I allowed to change the input and enter some keyword (which would actually help my users)?
Am I at least allowed to say something like: "Try Google" above the search bar?

I've seen this on lots of sites.

 

Thanks for linking to a page that prompts to install something!

Seems like a violation to me.

 

I'm sorry.
I just found this one. I removed the link.

Here is another one. Not modifying the input, but still something like "try google"

www.nightskyobserver.com/astronomy-software.php

 

the site above is just a custom google search code, not the adsense one.

 

This was just an example. I've seen lots of adsense bars with some information like "try google".

Is this allowed (at least)?

 

Googs seems to be very lenient when it comes to their search bar. I've seen "customized" versions of it everywhere. Personally I haven't touched mine -- I'm making too much off Adsense to risk getting kicked out for something so minor.