Learn German: Jeden Tag geschieht exakt dasselbe. - Exactly the same thing happens every day.

In this sentence, dasselbe acts as a pronoun for a generic, abstract concept or situation rather than replacing a specific noun. In German, abstract concepts or general events default to the neuter gender. It acts as the subject of the sentence, so it is in the nominative case.

Why is dasselbe written as one lowercase word? Doesn't it act like a noun here?

While it translates to "the same thing", the words derselbe, dieselbe, and dasselbe are pronouns, so they are traditionally written in lowercase. They are also always written as a single combined word, unlike English where "the" and "same" are separate.

Would it be correct to say das Gleiche instead of dasselbe?

Strictly speaking, dasselbe means the exact identical thing, while das Gleiche refers to things of the exact same type (like two people wearing the same jacket). In everyday spoken German, people often mix them up, but dasselbe is perfect here to emphasize that the daily routine is an unbroken repetition of the identical event.

Why is Jeden Tag in the accusative case here?

When you state a definite time or frequency without using a preposition (like an or in), you must use the accusative case. Because the word for day is masculine (der Tag), it becomes jeden Tag.