Official Developer Program

For a standard iPhone you'll need to pay the US$99/yr to be a member of the developer program. You can then use the adhoc system to install your application onto up to 100 devices. The developer program has the details but it involves adding UUIDs for each of the devices to your application package. UUIDs can be easiest retrieved using Ad Hoc Helper available from the App Store. For further details on this method, see Craig Hockenberry's Beta testing on iPhone 2.0 article

Jailbroken iPhone

For jailbroken iPhones, you can use the following method which I have personally tested using the AccelerometerGraph sample app on iPhone OS 3.0.

Create Self-Signed Certificate

First you'll need to create a self signed certificate and patch your iPhone SDK to allow the use of this certificate:

1. Launch Keychain Access.app. With no items selected, from the Keychain menu select Certificate Assistant, then Create a Certificate.

   Name: iPhone Developer
   Certificate Type: Code Signing
   Let me override defaults: Yes

2. Click Continue

   Validity: 3650 days

3. Click Continue

4. Blank out the Email address field.

5. Click Continue until complete.

   You should see "This root certificate is not trusted". This is expected.

6. Set the iPhone SDK to allow the self-signed certificate to be used:

   sudo /usr/bin/sed -i .bak 's/XCiPhoneOSCodeSignContext/XCCodeSignContext/' /Developer/Platforms/iPhoneOS.platform/Info.plist

   If you have Xcode open, restart it for this change to take effect.

Manual Deployment over WiFi

The following steps require openssh, and uikittools to be installed first. Replace jasoniphone.local with the hostname of the target device. Be sure to set your own password on both the mobile and root users after installing SSH.

To manually compile and install your application on the phone as a system app (bypassing Apple's installation system):

1. Project, Set Active SDK, Device and Set Active Build Configuration, Release.

2. Compile your project normally (using Build, not Build & Go).

3. In the build/Release-iphoneos directory you will have an app bundle. Use your preferred method to transfer this to /Applications on the device.

   scp -r AccelerometerGraph.app root@jasoniphone:/Applications/

4. Let SpringBoard know the new application has been installed:

   ssh mobile@jasoniphone.local uicache

   This only has to be done when you add or remove applications. Updated applications just need to be relaunched.

To make life easier for yourself during development, you can setup SSH key authentication and add these extra steps as a custom build step in your project.

Note that if you wish to remove the application later you cannot do so via the standard SpringBoard interface and you'll need to use SSH and update the SpringBoard:

ssh root@jasoniphone.local rm -r /Applications/AccelerometerGraph.app &&
ssh mobile@jasoniphone.local uicache

As Kevin points out, URL Schemes are the only way to communicate between apps. So, no, it's not possible to launch arbitrary apps.

But it is possible to launch any app that registers a URL Scheme, whether it's Apple's, yours, or another developer's. The docs are here:

Defining a Custom URL Scheme for Your App

As for launching the phone, looks like your tel: link needs to have least three digits before the phone will launch. So you can't just drop into the app without dialing a number.