The key issue for realizing the potential of carbon nanotubes has always been, and still remains, a better control of their growth and in particular the selective control of their chirality related to their electronic properties. This work aims to address the in-situ synthesis and characterization of individual carbon nanotubes by field emission to better understand the mechanisms of nucleation and growth that determine their chirality. We have developed a field emission microscope coupled to a CVD reactor (Chemical Vapor Deposition) to observe directly the catalytic growth of individual carbon nanotubes on metallic tips. We found that nanotubes often turn axially during growth, thereby supporting a model of "screw dislocation". Detailed analysis of results shows that we directly observe the atom by atom growth of one individual single wall nanotube with addition of a carbon dimer to the base. In parallel, certain samples were characterized by in-depth field emission studies. For this we established a protocol of bonding individual nanotubes at the apexes of metal tips under optical and scanning electron microscopies using a nanomanipulator. Their temperature dependence at very low current has been demonstrated with an electron counter to identify the various fields of electron emission. Analysis of energy distributions revealed an induced heating phenomenon that can lead to temperatures of about 2000 K at the end of the nanotube subjected to strong fields that create high current emission.