kono doa ha hurui node, muri ni akenaide kudasai.

The spaces are just for learners. Normal Japanese is usually written without spaces:

このドアは古いので、無理に開けないでください。

Textbooks and beginner materials often add spaces to make it easier to see where words and particles begin and end.

この means this and must come directly before a noun.

• このドア = this door

You cannot usually use この by itself as a standalone noun. If you want to say this one, you would use これ instead.

• このドア = this door
• これ = this one

は marks ドア as the topic of the sentence.

So このドアは means something like:

• As for this door...
• This door...

The sentence is then giving information about that door: it is old, so please do not force it open.

Using は is natural here because the speaker is talking about a specific object and making a statement about it.

Because 古い is an i-adjective.

With i-adjectives, you connect directly to ので:

• 古いので = because it is old

You do not add だ after an i-adjective.

Compare:

• 古いので = because it is old
• 静かなので = because it is quiet

In the second example, 静か is a na-adjective, so it needs な before ので.

ので means because or since. It gives the reason for the request.

So the structure is:

• このドアは古いので = because this door is old
• 無理に開けないでください = please do not force it open

Compared with から, ので often sounds a little softer, more explanatory, and less direct. That fits well in polite requests.

Yes, it could:

• このドアは古いから、無理に開けないでください。

This would still be natural and correct.

The difference is mainly nuance:

• ので = a bit softer, more formal, more explanatory
• から = a bit more direct, conversational

In a notice, instruction, or polite warning, ので is very common.

無理に means forcibly, by force, or unreasonably / too hard depending on context.

Here it means something like:

• don’t force it open
• don’t try to open it by force

The base word is 無理, which can mean impossible, unreasonable, or forcing something beyond what is natural.
Adding に turns it into an adverb-like expression:

• 無理 = unreasonable / impossible / force
• 無理に = forcibly / by force

The に turns 無理 into an adverbial expression modifying the verb 開けないでください.

So:

• 無理に開ける = to open by force / to force open

This is very common with some nouns and na-adjectives when they are used adverbially.

For example:

• 静かに話す = speak quietly
• 丁寧に書く = write carefully
• 無理に開ける = force open

This is a very common polite way to say please do not do X.

Breakdown:

• 開ける = to open
• 開けないで = do not open
• 開けないでください = please do not open

So the pattern is:

• verb nai-form + でください = please don’t do it

Examples:

• 入らないでください = please do not enter
• 触らないでください = please do not touch
• 開けないでください = please do not open

In this sentence, because of 無理に, the meaning becomes please do not force it open.

This is about the difference between transitive and intransitive verbs.

• 開ける = to open something
• 開く = something opens

Here, a person is being told not to open the door by force, so Japanese uses the transitive verb 開ける, because someone is acting on the door.

Compare:

• ドアが開く = the door opens
• ドアを開ける = open the door

In your sentence, the understood object is the door, so 開けないでください is the natural choice.

Yes, it is polite.

開けないでください is a standard polite request, and ので makes the reason sound calm and explanatory. The whole sentence sounds like something you might hear or read:

• on a sign
• from a staff member
• in a public notice
• in a safety warning

It is not super formal, but it is definitely polite and appropriate for everyday public instructions.

Yes, ドア is very normal and common. It is a loanword from English door.

Another word is 扉（とびら）, which also means door, but it can sound a bit more formal, literary, or specific depending on context.

So:

• このドアは古いので… = very natural in everyday speech and signs
• この扉は古いので… = possible, but less everyday in many situations

For a typical spoken warning or notice, ドア is probably the most natural choice.