ame de keikaku ga dainasi ni natta.

Here, で marks the cause/reason: because of the rain.

This is a common use of で with things like:

• weather
• accidents
• illness
• natural causes

So 雨で means due to the rain or because of the rain.

It is not the location use of で in this sentence.

Because 計画 is the thing that became ruined, so it is the grammatical subject of 台無しになった.

The pattern is:

• X が Y になった = X became Y

So:

• 計画が台無しになった = the plan became ruined

If you used を, you would normally need a transitive verb, such as:

• 雨が計画を台無しにした = the rain ruined the plan

In your sentence, the structure is intransitive: the plan became ruined.

台無し means something like:

• ruined
• spoiled
• messed up
• wasted

It is often used when something good, valuable, or carefully prepared is destroyed or spoiled.

Examples:

• 努力が台無しになる = one’s efforts go to waste
• せっかくの旅行が台無しだ = the trip is ruined

So in this sentence, 台無し expresses that the plan was spoiled.

Because に marks the resulting state in the pattern:

• noun / な-adjective + に + なる

This pattern means become ...

So:

• 台無しになる = to become ruined
• 静かになる = to become quiet
• 元気になる = to become healthy / energetic

Here, 台無しに shows the state that the plan ended up in.

なった is the past tense of なる.

• なる = to become
• なった = became

So 台無しになった means became ruined or ended up ruined.

The past tense is used because the ruining already happened.

Yes, but the meaning and structure change.

• 計画が台無しになった
  = The plan got ruined / became ruined

• 誰かが計画を台無しにした
  = Someone ruined the plan

So:

• 〜になる focuses on the result/state change
• 〜にする / 〜にした focuses on the agent causing it

In your sentence, Japanese chooses the more natural intransitive phrasing.

It could say 雨のせいで, and that would also be natural.

The difference is nuance:

• 雨で = neutral because of the rain
• 雨のせいで = more explicitly because of the rain, and that’s unfortunate / to blame

So 雨のせいで計画が台無しになった sounds a little stronger and more emotional.

Your original sentence is simpler and slightly more neutral.

Using が here presents 計画 as the grammatical subject of the change:

• 計画が台無しになった

If you use は, the nuance shifts to making 計画 the topic:

• 計画は雨で台無しになった

This can sound like:

• As for the plan, it was ruined by the rain
• possibly with contrast, depending on context

Both are possible.
The version with が is a very straightforward description of what happened.

No, Japanese word order is fairly flexible because the particles show each word’s role.

These are all possible, depending on nuance:

• 雨で計画が台無しになった
• 計画が雨で台無しになった
• 計画は雨で台無しになった

The most important thing is keeping the predicate together at the end:

• 台無しになった

So the order can move somewhat, but the particles must stay correct.

There may be missing context, but grammatically the subject here is already 計画.

So the sentence literally centers on:

• The plan became ruined because of the rain

Japanese often leaves out information like:

• whose plan it was
• who was affected
• who is speaking

If needed, you could add that:

• 私たちの計画が雨で台無しになった
  = Our plan was ruined by the rain

But without that, the sentence is still complete and natural.

Yes. It is often used for both.

Physical examples:

• ケーキが台無しになった = The cake was ruined
• 服が台無しになった = The clothes got ruined

Non-physical examples:

• 計画が台無しになった = The plan was ruined
• 気分が台無しになった = My mood was ruined
• 努力が台無しになった = The effort went to waste

So in your sentence, it refers to a plan, not a physical object, and that is completely natural.