For the search bar:
1) Install the addon Add To Search Bar
https://addons.mozilla.org/en-US/firefox/addon/3682
2) Restart Firefox
3) Go to your AdSense search page
4) right click on the the search box and press Add to Search Bar
5) Choose a name and icon and press okay

To modify the url bar you can easily go to your config page in firefox.
Here are instructions:

1) Do a search on your adsence account
2) Copy the url from the search
(e.g. http://myadsencesearch.com/search?q=Search Term&option=32
All these will be your own values and Search Term will be what you searched for)
3) Modify the url so ?q=Search Term is at the end there is a few rules so follow these guidelines:
a. ? must be after /search
b. if there is no ? before q= then there must be a &
c. ?& does not go together:
If it is after the /search then delete the &
If not delete the ?
So the example above will read:
http://myadsencesearch.com/search?option=32&q=Search Term
4) Remove the Search Term
So it will say now:
http://myadsencesearch.com/search?option=32&q=
5) Visit this page in your address bar: about:config
6) In the filter bar enter: keyword.URL
7) Modify the value of keyword.URL
(Double click or right click and press modify)
8) Paste the url in (http://myadsencesearch.com/search?option=32&q=
9) Press okay and perform a search
Source(s):
https://addons.mozilla.org/en-US/firefox/addon/3682
https://addons.mozilla.org/

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Go to your Adsense Account page & create your search unit for your firefox & implement it
Source(s):
http://www.adsense.com
http://adsense.google.com

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