What apparent sizes of the sun an Earth like planet can have? What is the smallest and largest sun an Earth like planet could have in its sky? What kinds of stars are those?

I saw this video and thought, yeah, some of those stars are really big in absolute terms, but Earth would have to be orbiting them proportionally further to keep the climate, making them smaller in the sky, so the video is not accurate.
I'll make a very simple dimensional calculation here. 

Total power from of a star with radius $R$ and temperature $T$: 

$$ P_{tot} \ = \ R^2 \ T^4$$

Flux $I$ (power per unit area) at an orbital distance $r$:

$$I \ = \ \frac{R^2 \ T^4}{r^2} \ = \ T^4 \ \left( \frac{R}{r} \right)^2$$

Apparent size (radians, small angle approx):

$$\theta \ \approx \frac{R}{r}$$

So:

$$\theta \ \approx \ \frac{\sqrt{I}}{T^2}$$

Surprisingly, for a fixed incident flux of light (ignoring different planetary warming effects of different wavelengths) the apparent size of a sun viewed from a star varies roughly as the inverse square of its temperature, and does not depend on the actual size of the star.

Your milage may vary.

Using Wein's dispacement law which relates the wavelength of maximum spectral radiance of a blackbody $\lambda_{max}$ with its temperature $T$ using Wien's displacement constant $b$:

$$\lambda_{max} \ = \ \frac{b}{T}$$

The apparent size scales with the square of the peak wavelength of a star's blackbody spectrum. 

$$\theta \ \approx \ \lambda_{max}^2 \ \sqrt{I}$$

Yay! Reddish stars will appear much larger than bluish stars - the result we were all expecting.

And if you'd like do some landscaping, the 2008 Scientific American article The Color of Plants on Other Worlds is a good read in stellar spectra, atmospheres, and photosynthesis.