lhapdf5

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a)
"""
Can you tell me how to install the PDF in the lhepdf5 and where to keep ? There are two directories.
"""
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In order to specify an lhapdf-version in MG5_aMC, you should set the option 'lhapdf' to the full-path to the 'lhapdf-config' executable. (you can do this by either using the command

'set lhapdf <full_path_to_"lhapdf-config">'

in MG5_aMC interactive interface or by directly modifying this option in the configuration file

'<MG5_install_path>/input/mg5_configuration.txt'

Now, if you don't have the directories 'bin' and/or 'share' in the 'lhapdf5' directories (as it seems to be your case) then it means that lhapdf5 installation failed (but MG5aMC does not reports this because it only checks for the existence of the libraries which are there).
You can find the cause of the problem in the lhapdf5_install.log file placed in your 'lhapdf5' install directory.

I stress that when installing a dependency with MG5_aMC, you can install it with the option '--keep_source' which will keep the lhapdf5 source (i.e. in the directory <MG5_install_path>/HEPTools/lhapdf5_src) from which you can find the configure command (in the file ./config.log).

On a mac, I have similar problems with LHAPDF5 as it forces the use of clang++ even though I have GNU++ for building the octave interface.
For this reason, I have to disable it when calling './configure' of lhapdf5, using the additional option ' --disable-octave'.
Please confirm that this is your problem as well. In any case, I will now automatically add this option since it seems to cause issues.

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b)
"""
*** Boost is too old for this compiler version. gcc-mp-4.8 needs boost > 1_47.
*** See http://code-muse.com/2013/08/06/boostforeach-and-compiler-bugs
"""
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In the file 'lhapdf6_install.log' in the <MG5_install_path>/HEPTools/lhapdf6 folder can maybe give more context.

What you should also try is to install lhapdf6 again with the option '--keep_source', that is:

MG5_aMC> install lhapdf6 --keep_source

You can then go to the directory:

<MG5_install_path>/HEPTools/lhapdf6_src/LHAPDF-6.1.6

And you can see what configure options where specified in the file 'config.log'. You should be able to confirm that the newly installed version of boost was correctly specified, i.e. that is (in my case):

./configure [...] --with-boost=/Users/valentin/Documents/Work/MG5/HEPTools/boost [...]

In my case I can then see lhapdf6 correctly identifying the version of my boost headers, i.e. later in config.log there is:

[...]
configure:16345: checking for Boost headers version >= 1.41.0
[...]

So if you confirm that you indeed have the newly install BOOST path specified at the configuration stage, but you still face the LHPADF6 installation error that you mentioned, then you should contact directly the LHAPDF6 authors with the description of this issue.