." to avoid problems with partial ionization of most analytes " : this means that we want to have a total ionisation of the analyte ?
In general, you want to start with either total ionization or total suppression. Partial ionization runs the risk of robustness problems, since the degree of ionization can change with small variations in pH.
which means that with a pH of approximately 2.1 all the NH2 groups will be ionised and takes their acid form that is NH3+ ,
Yes
and thanks to that, it become easy to detect them (and then to detect the ferrocenic amid) ?
No, the comment did not refer to detection but rather to potential variations in retention.
Because , in HPLC , we can't detect all analytes , can we? So we use some reagent that react with the analytes to make its detection possible, use we?
"post-column reaction" detection is used in HPLC, but usually for compounds which cannot be conveniently detected any other way (which does include many amines). That's not what the use of TFA is about.
"TFA is a weak ion-pairing reagent"
In one "mental model", the CF3 group is somewhat hydrophobic, so presumably some of the TFA sticks to the surface of your reversed-phase packing. Your cation can then interact with the carboxyl group via an ion-exchange type of mechanism. CF3 is not very hydrophobic, and the carboxyl group is only partially ionized, which is why TFA is a "weak" ion pairing reagent. The effect has been well documented with peptides, in which case the relative retention of basic peptides increases with increasing TFA concentration.
For a moment i thought that in presence of TFA , i would have a cation and an anion : R-NH3+ , CF3COO- , that why it becomes possible to detect the amid by HPLC.
You do, and the other "mental model" is that these two neutralize each other to form a relatively hydrophobic "ion pair" which can be retained on a reversed-phase column. As with the comment about pH, however, this has nothing to do with detection, but rather with retention.