Is it legal to fire someone just because they are looking for a new Job? I was looking to find a better paying job since they didn't pay well where I worked and even tried talking to them with no luck to change it.
There was nothing stating about me doing a bad job or being disrespectful fact is I got praised for doing well many times by the people I assist as I work as a helpdesk support person. do I have any grounds for being fired unjustly for a legal suit?

No grounds for a suit at all.

There is a reason why people don't talk about interviewing while at work. Because your employer may take it to mean that you aren't a good influence on the other workers.

Nope, no wrongful termination here. Sorry.

Or it could mean that the person is upset and an upset computer support person is a risk.

I don't know.

From the computer support people I have spoken to, some companies apparently believe it is a job qualification.

Actually yes, we sometimes joke that if you don't have an attitude problem, you can't possibly be a good support person.