Vocal Tone and Vocal Range

On Tuesday we had a singing lesson, where we learnt about how to improve your control vocals and the tone of your singing voice (a sound of distinct pitch, quality, and duration; a note). We learnt that engaging yuour abdominal muscles while singing, as opposed to your singing from your throat, results in the best possible quality to your voice.

Here is a link to a web page that describes what vocal tone is:
http://www.dummies.com/how-to/content/defining-tone-in-singing.html

Here are some videos that also decribe the meaning of  'vocal tone' and the techniques that you can use to improve it. They also give you some vocal excersises, which I find very helpful:
http://www.youtube.com/watch?v=zxt4TcAkkSk
http://www.youtube.com/watch?v=z1DSwxVv1f8
Another great exercises, for this is lying flat on your back and singing. This way, it is very difficult for you to lift your shoulders, as you breathe from your chest. This forces you to breathe from your stomach, which should make it easier to sing using your abdominal muscles.

Here is a youtube video of me singing through my throat.
https://www.youtube.com/watch?v=Wykmd-N8aYk
Here is a video of me singing, while engaging my abdominal muscles.
https://www.youtube.com/watch?v=acc5hccVepw

I have been using online tutorials, as well as exercises that I have learnt at college to improve my range (vocal range is the measure of the breadth of pitches that an individuals voice can produce). Specifically, my higher range. Here is one of the videos that I have used:
http://www.youtube.com/watch?v=L-zv1dpom94
I especially find lip trills helpful as they allow me to go through all of my range very easily.

https://www.youtube.com/watch?v=kPkuFCKQoJE
https://www.youtube.com/watch?v=EX3EQjt_kzE
This youtube videos, show the improvement I have made on my vocal range so far. At times , I sound like I'm straning in the first and in the second I sing out of tune, which I could have improved by engaging my stomach muscles more. It is the highest I can currently sing in my chest voice (Your singing voice closest to your speaking voice). I can however sing a lot higher in my head voice (The higher range of your voice, where the vibrations are felt in the head). The riffs at the end went wrong (

a riff is a short repeated phrase in popular music and jazz, frequently played over changing chords or harmonies or used as a background to a solo improvisation).

I need to keep using vocal exercises to improve my range in my chest voice.