Potential energy and mass a) Can we convert energy to mass (matter) in every day life?
b) When we charge a phone battery, its mass (weight) increases according to $E = mc^2$ . Does it mean we convert energy to matter? If not, how its mass increases?
 A: 
a) Can we convert energy to mass (matter) in every day life?

There are two ways this question can be understood; 1) can we add mass to existing matter, and 2) can we create new matter.

*

*Yes - we can increase mass of an existing object by putting in some energy, such as heat energy, or electric energy. The increase in mass is almost always extremely small and hard to detect. Both energy and mass of the body increases in this process. There is no "conversion" of energy to mass; there is only ever conversion of form of energy, such as from electric potential energy to kinetic energy of thermal motion. The number and quality of matter particles stays the same.


*Not in everyday life, but in special high energy events, such as particle collisions in colliders or in atmosphere due to cosmic rays, some matter particles appear to be created. We believe this happens in line with the Einstein relation $\Delta m = \frac{\Delta E}{c^2}$.

b) When we charge a phone battery, its mass (weight) increases according to =2. Does it mean we convert energy to matter? If not, how its mass increases?

This is the case 1) above. Mass of battery increases but there is no matter creation. Electric energy going in is not accompanied by creation of new matter particles. The mass increases due to increased chemical energy inside the battery.
A short though imprecise statement to understand this is that adding energy means adding mass, and removing energy means removing mass, according to the Einstein formula
$$
\Delta m = \frac{\Delta E}{c^2}.
$$
A: General Relativity suggests that energy contributes to the space-time curvature that we call gravity.  If you add energy to a system, you increase its resistance to acceleration. The simple explanation is that energy has mass. But then, that gets into the question: What is mass? Or even: what is matter?
A: 
a) Can we convert energy to mass (matter) in every day life?

Not really.It is true that special relativity is always valid, but for the velocities and energies involved in everyday life classical Newtonian mechanics and classical electricity and magnetism describe our energy considerations to a very great accuracy. Special relativity would give correction below our possible measurement errors.

b) When we charge a phone battery, its mass (weight) increases according to E=mc2

Not really, the amount of increase in the mass is too small to measure.the $m$ in $E=mc^2$ is the inertial mass of a moving body, the resistance to further accelerations, not the intrinsic mass of the body. The special relativity effect is not measurable.

. Does it mean we convert energy to matter? If not, how its mass increases?

The inertial mass does not increase within the possible measurement errors.
The inertial mass is equal to the intrinsic mass of a body when the body is at rest. To see this in the lab one has to go to nuclear reactions, how energy can be released according to special relativity equations from , for example, a Uranium nucleus decaying into smaller mass nuclei, the difference becoming kinetic and radiation energy.
GPS is in every day use, and there the equations of special and general relativity , due to the masses and velocities of earth and satellites have to be used for corrections in order to get the accuracy we see.
