Depends on how much smaller my planet was. If my Earth were too small to create enough gravity to hold an atmosphere or an ocean, I would not be here -- indeed, no life would be here -- to get upset over too small a planet.
I'm sure it's the same situation on your planet.
Planets orbit stars, not other planets. A planet-like object that orbits a planet is a moon.
Mercury
Eris is not a planet; it is a dwarf planet. It is much smaller than Earth.
No known planet is smaller than Mercury since Pluto was reclassified as a Dwarf Planet.
Jupiter is the largest planet, so all of the other planets are smaller.
Mercury is smaller than Titan, but Titan is a moon, not a planet.
If the planet is smaller, then it can't have the same size. If you assume that a smaller planet has the same density as Earth (and therefore less mass), its surface gravity will be smaller. If you assume that a smaller planet has the same mass as Earth (and therefore more density), its surface gravity will be greater. This is because we would be closer to the planet's center - or to the planet's matter in general.
Mercury, Venus and Mars are all smaller than the Earth. If the question is referring to the US as in the US of A, then no planet is smaller.
Yes
Mars is the only planet which is both smaller and colder than the Earth.
Jupiter is not a star. It is a planet. However, there are stars that are smaller than the planet Jupiter.
No known planet is smaller than Mercury since Pluto was reclassified as a Dwarf Planet.