Does English allow to call a planet "star" too?
Only in one very limited sense and that is when referring to Venus.
Due to its orbital radius, size, etc, planet Venus is often visible in the morning around sunrise and in the evening around sunset. It is referred to as "the Morning Star" or "the Evening Star". These names are nowadays nicknames or used in poetry or to make speech more interesting.
Ancient observers seeing points of light in the sky named them stars. Some of these stars, such as Venus, were observed to appear in different positions compared to other stars: They were said to wander. Hence they were called asteres planetai with asteres meaning "star" and planetai meaning "wandering". Planetai has since been introduced as "planet" and it no longer has meaning as "a wandering point of light in the sky" but as "a ball of rock or gas (of a certain size) that orbits a star". (Please be aware that there is no good definition of some important terms in astronomy.)
While many people learn as children that planets were called wandering stars in the past, calling planets stars is abnormal and wrong today.
what I'd like to know is whether it's possible to call real planets in the space in such a way, or there is a blanket term roughly covers star, planet, satellite and asteroid (but not nebula or galaxy).
You can see 星 can replace "planet" (惑星) in every situation unless you have to tell planets from other bodies. Is it possible in English?
There is no blanket term.
In astronomy, due to the significant variation in mass, energy output, life cycle, often diameter of astronomical objects there is no collective term that refers to "stars (self-luminous bodies) and planets and asteroids and moons (natural satellites) and comets". There has simply been no need or desire for such a term.
Humans have only been aware of asteroids for a very short amount of time (215 years). They were discovered by scientists and for about 50 years "asteroid" (once the term was invented) and "planet" were used interchangeably in the scientific community but asteroids weren't a topic for general conversation. No popular term arose to refer to both at the same time since scientists saw them as different and needing to be distinguished and the public was largely unaware of their existence.
Comets were called, to some extent, stars by the ancients. They were seen as bad omens and were called "disasters" ("dis" evil/bad, "aster" star). Nowadays education is such that many children and adults are aware that comets are balls of ice and rock, often with a tail -- some even know the tail is caused by solar radiation ablating the nucleus -- and are distinct from planets and stars.
Aside from Earth's moon, which has never to my knowledge been called a star in English, other moons have only been known for about 406 years. Galileo called those early discoveries stars but that name has long since been abandonned in favour of satellites or moons.
Contrary to that dictionary, I am not aware of any instance in Western/Ptolemaic astrology where stars can be called planets. Planets are called "planets" and that term includes Pluto, the sun and moon may be called "luminaries", there are calculated positions called "nodes" where the moon's orbit intersects the ecliptic. Stars scarcely feature except as the backdrop against which the planets/luminaries/etc move.
A quick search showed up only the plural word stars as in "what's in the stars?" and "it's written in the stars". It appears "stars" is being used as a metonym to mean "prognostication by observing astronomical bodies". Maybe "star" was used in astrology historically but I don't think it's widely used now.