Yes, you can customize your search. Goto Setup >Tab Settings >Search Layout >select the module/tab >edit and select the fields that you would like to search. Please Note: You cannot select more than 6 fields.
You can restrict this at Profiles. Goto Setup >Admin Settings >Profiles Edit the standard profile or create a new profile and un-check the option Customize Zoho Support under Admin Options. Associate this Profile to the Support Agent (Setup >Admin ...
Yes, you can customize the Notification Alert template. Goto Setup > Notification settings >Notification Rules > click Customize Template link to make the changes.
To customize default e-mail templates, Goto Setup> Templates > Email Templates > edit the template and make changes > Click Save. For more refer Templates