For the history on the unit of time have a look at this link.
The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.
In the same click on meter to get the definition of a meter.
The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.
Note that the effect of this definition is to fix the speed of light in vacuum at exactly 299 792 458 m·s-1.
Have a look at the paragraph Experimental measurements of the elementary charge . The oil drop experiment has been repeated in innumerable under graduate lab courses.
The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram
Once the charge of an electron is known, a simple experiment with a magnetic field and a measurement of the radius will give its mass.
In this image of a bubble chamber materialization of an electron positron pair
there is energy loss due to electromagnetic collisions of the electron .When the experiment is carried out in vacuum with electrons the mass can be measured.
It is very seldom in physics experiments that two quantities can be measured at the same time. The measurements are done sequentially building logically on previous knowledge.
Here is an experiment measuring h.
The experiment used a black body approach to experimentally measure Planck’s
reduced constant, by using the Planck Radiation Law, which relates the intensity and wavelength of light to the temperature of the emitting black body. The measurement was accomplished by using a simplified detection system involving a photodiode and diffraction grating to measure the intensity of emitted light as a function of the wavelength. From the experiment it was found that the value h_bar of was 2.8±1.5x10^-35 Js.