Why installation "update" my Firefox and reboot my machine?

I just came across the project and downloaded the latest version 26.2.1. Is kind of odd that it tells me that will update my Firefox instalation THAT IS ALREADY UPDATED and asks me to reboot my machine. Very suspicious, indeed. I´m pretty sure I just want to create and edit files and Firefox have nothing to fo with that to be modified. Is this the normal behavior of the software? Kind of “take over my web navigation” like Microsoft does?

Yes it is normal. Additionally, it doesn’t tell you “it will will update your Firefox installation” - it tells you “Firefox uses files that need to be updated”, which is different. It is “we use a shared component; Firefox uses the same shared component; we have to update it”. Or it can be “Firefox loaded my DLL; I cannot update it”.

See tdf#69066 and its See Also.