A convert is suppoed to accept the ol mitzvot, the burden of halacha but does this mean an explicit intent to follow the mitzvot or simply the acceptance that there is a punishment if the mitzvot are ...
May a non-Jew or a person who is in the conversion process don tefillin? If not, what are the reasons that they cannot?
If a fellow converted (his children remained gentiles) and prior to his conversion he had children - has he fulfilled the Mitzva of Peru U'Revu? (sources)