Is there a way to generate an alert email whenever we have a new lead?

Here is the scenary:

We have a new lead, then an email alert is sent to the staff responsible to qualify that lead to start the qualification process right away

If possible, how can I do this, is it done by creating a contact process?

Unfortunately, there is no way to do this right now in the base product. However, there are plenty of 3rd party products out there - look for KnowledgeSync from VineyardSoft or Orbis TaskCentre.

Essentially, these products can all "watch" your database for events to occur. The one you mention above is just one - but I'm sure you can think of plenty of others ! So, by using a 3rd party app like the ones mentioned you can watch for any event and then take action. As opposed to a "point" solution like this one. However, if you really need just this - you can have your BP customise the system to run this event especially given the conditions you suggest.

Regards
Mike