Learn English – “He’s finally joined to the gym” or “He’s finally joined the gym”

In, at, on are prepositions of place. Generally,

• on is used for position on a surface,
• at for a specific place or point,
• in for enclosed or surrounding space.

Walk-in closet is a closet that is large enough to walk around in - in other words, an enclosed space. Hence, you joined Tom in Flora's walk-in closet.

• I can't make it home CORRECT

This means you are unable to reach this destination. Home could refer to the building, or the area where you live; e.g., village, city, country. When used as an adverb of place, home requires no preposition

An Australian holidaymaker: I can't wait to get back home (home = Melbourne, Australia)

• I can't make it to home UNLIKELY but not impossible

In this sentence we have to identify what home might be referring to. It could be short for home base (think of a baseball player running to home base) or the home plate

With the Yankees prepared for the long play, Taylor instead bunts, allowing Hayes to make it to home safely and win the game.

• There was heavy traffic but I finally made it to work CORRECT

This means the speaker managed to arrive at his or her workplace despite the traffic. Work and workplace are nouns, and the preposition to is used to express motion or a direction toward a point or thing.

• There was heavy traffic but I finally made it work INCORRECT

This sentence is grammatical but it has a completely different meaning. It means that the speaker managed to make something work i.e function despite the heavy traffic. In other words, the speaker repaired something that was broken or not functioning properly. And in the sentence, work is used a verb

My watch is broken, can you make it work again?
His phone doesn't work unless he goes to a high point