atarasii doa kara heya ni haitte mo ii desu ka?

The pattern verb-て form + もいいですか is used to ask for permission.

• 入ってもいいですか？ literally means “Is it okay if I enter?” or “May I enter?”

Because when you use 〜てもいいですか, you attach it directly to the て-form of the verb.

• 入る becomes 入って in the て-form, and then you add もいいですか.

Here から marks the starting point of the action (“from the new door”).

• It is not the “because” から, but the location-of-origin marker.
• You’re asking “May I enter from the new door?”

The particle に indicates the destination or goal of movement.

• With verbs of motion like 入る (to enter), に marks “into” or “to.”
• So 部屋に入る means “to enter the room.”

In Japanese, い-adjectives and な-adjectives both directly precede the noun they modify.

• 新しいドア = “new door.”
• The adjective always comes before the noun in the phrase.

You could say ドアで入ってもいいですか, but that changes the nuance:

• ドアで would mark the door as the location where the action happens (“May I enter at the door?”).
• ドアから stresses the point of entry (“May I enter from the door?”), which is more natural when talking about going through an entrance.

Japanese often omits subjects when they’re clear from context.

• In a permission request, it’s understood you’re asking about your own action (“May I …?”), so you don’t need to say 私は.