OffSimmons

No problem.
Dispatch we are Code 4.

Could anyone make a texture for the unarmed buzzard? Something kind of like the pictures below.

No this isn't possible using the API, and it is not a behavior we'd want to encourage.
That being said, it isn't difficult to setup a keybind for development that will only trigger your own callout (using the StartCallout API feature).

Its impossible to disable them because they are just one no more "Pursuit Callout" so you can install more mods to feel interested
Its a stock option with the game as the keyboards key bindings (You Can Not Change It)

Some low-grade research would reveal that we've always been LCPDFR.com, and that our LSPDFR.com is just a redirect.

You have to create it.

dispatch we are code 4 i will be 10-8

Make sure the ragehooksdk that your project references is the same one you're using in GTA. If your project is trying to include the ragenativesdk that it shipped with, then chances are it's not the same rage hook version you're using in game

Robber.Inventory.GiveNewWeapon("WEAPON_PISTOL", 500, true);

You have to wait until ELS is released 

It's not possible to disable them but in 0.3.1 was added the API function StartCallout, you can use it like this:
     LSPD_First_Response.Mod.API.Functions.StartCallout("yourCalloutName");
 
"yourCalloutName" is the name you have set in the CalloutInfo attribute.

Here you can find the API Quick Start Guide & Example Project.
Download and extract this to a location of your choosing, be careful to read the guide fully and read the comments in the example project.
The project itself requires Visual Studio and is written in C# which is what we recommend.
Over time the API will change and I'll try to update this with each change.
NOTICE: If you have any questions regarding API usage or you need help with particular problems, please create a thread in the API Development section.
Please title your new threads with an accurate but very summarised description of your problem. A set of FAQ's will be added to this post to help clear up common problems.
This new thread will be locked and updated with a changelog each time API functions get amended or added.
Changelog
23/Jul/15
• Added API function to play scanner audio using position to the example callout, updated references to default to RPH 0.20 and LSPDFR 0.2a.
APIExample.zip 
LSPDFR API Start Guide.pdf