It is not assur to speak while wearing tefillin. it’s assur to engage in frivolous or mundane conversation, but if it’s for a mitzvah then it’s ok, as you long as you’re not talking during davening.
when removing, there is a custom not to interrupt, but the practice is not accordance with this custom.
“Not that it is right, I have seen som people who raise their shel rosh slightly off their head so they can speak, and put back in situ when they have finished talking!” My rav said this is very bad b/c you’re obligating yourself in making a new bracha. you canNOT lift up the shel rosh.