There is certainly room for improvement there.
To start with, the first line should end with =False instead of =True , as that will save Excel from re-drawing itself every time your code changes a cell value etc.
Your section "'I- LOAD DATA FROM THE FORM" seems pointless based on what you have shown, as the variables aren't used - but I assume that they are used in code you haven't shown us.
I don't know why you have the code to set lastRow (which will be relatively slow), as that doesn't seem to be used either.
When specifying a cell it is better to specify the Sheet too (and preferably the Workbook), as that way Excel doesn't need to work out which one you intended, eg:
..doing that also means that you don't need the .Activate line, which slows things down.
Worksheets("Log").Range("A" & MyRow).Value = MyCoder
In terms of speed setting the values of cells individually is very poor (because Excel re-calculates everything after each one), it is much better to set them all at once, which you can do using an array, eg:
The formulas at the end could also be done in a better way, but I would need to do a bit of research to work out what your current code is achieving.
Worksheets("Log").Range("A" & MyRow & ":P" & MyRow).Value = _
Array(Array(MyCoder, MyCodingDate, MyChannel, MyProgramName, _
MyProgramDate, MyPresenter, MySegment, MySubjectType, _
MySubjectDesc, MyNewsType1, MyNewsType2, MyNewsGrid _
MyLeader, MyLeaderInstitution, MyLeaderCountry, _
However... the majority of these recommendations will have a very small effect, as the code you have shown doesn't actually do that much (in terms of the time it would take to run). I suspect that step 3 is where the most time is used.