1. They are not both fundamental, a mole is defined as the amount of substance that contains an equal number of elementary entities as there are atoms in 0.012kg of the isotope carbon-12. So the mole is defined in terms of the kg.
2. This is essentially Arnold Nicolaus' project (described in the article). He wants to define the kg as the mass of a certain number of atoms. But we don't yet have an accurate way of counting atoms, so if we pick a number (i.e. define Avogadro's number by fiat) today, then later when we count more carefully the mass of everything (denoted in kg) will fluctuate.
1. They are not both fundamental, a mole is defined as the amount of substance that contains an equal number of elementary entities as there are atoms in 0.012kg of the isotope carbon-12. So the mole is defined in terms of the kg.
2. This is essentially Arnold Nicolaus' project (described in the article). He wants to define the kg as the mass of a certain number of atoms. But we don't yet have an accurate way of counting atoms, so if we pick a number (i.e. define Avogadro's number by fiat) today, then later when we count more carefully the mass of everything (denoted in kg) will fluctuate.