unjeonhaneura jeonhwareul mos badasseo.

Yes. -느라 and -느라고 are interchangeable here. -느라고 is the fuller form that’s very common in speech; -느라 is a slightly shorter variant. Meaning and usage are the same in sentences like this:

• 운전하느라(고) 전화를 못 받았어.
• 운전하느라고 전화를 못 받았어.

All of these can express cause, but the nuance differs.

• 운전해서/운전하니까/운전하기 때문에 전화를 못 받았어. Neutral “because.”
• 운전하느라 전화를 못 받았어. Emphasizes being tied up doing something and strongly expects a negative/failed result. Sounds apologetic/explanatory.

Also, -아서/어서 and -(으)니까 work with adjectives too; -느라 is mainly for action verbs.

Attach -느라 to the verb stem of an action verb:

• 하다 → 하느라 (운전하다 → 운전하느라)
• 먹다 → 먹느라
• 씻다 → 씻느라
• 기다리다 → 기다리느라

With common irregulars, there’s typically no change because the suffix starts with a consonant:

• 듣다 → 듣느라 (not 들으느라)
• 걷다 → 걷느라
• 돕다 → 돕느라

For 하다-compounds, both 운전하느라 and 운전을 하느라 are fine.

Generally no; -느라 is for action verbs. There are a few idiomatic exceptions when the adjective implies being tied up, especially 바쁘다:

• 바쁘느라 전화를 못 받았어. (I was busy so I couldn’t answer.) For most adjectives, use -아서/어서 or -(으)니까:
• 피곤해서/아파서 못 갔어. (Avoid 피곤하느라/아프느라 in standard usage.)

No. -느라 explains a negative/undesirable result; it doesn’t combine with imperatives or suggestions.

• Natural: 회의하느라 늦었어요. (I was in a meeting, so I was late.)
• Unnatural: 회의하느라 일찍 오세요. (Don’t use -느라 with commands.)

Yes. The subject of the -느라 clause and the result clause should be the same.

• Natural: 내가 운전하느라 전화를 못 받았어.
• Unnatural: 친구가 운전하느라 나는 전화를 못 받았어. Use a different connector when subjects differ:
• 친구가 운전해서 나는 전화를 못 받았어. Or rephrase to keep the same subject:
• 내가 친구를 기다리느라 전화를 못 받았어.

Yes. Common phone collocations:

• 전화를 받다 = answer/take a call
• 전화가 오다 = a call comes in
• 전화를 하다/걸다 = make a call
• 통화하다 = be on a call

Yes. Elliptical use is natural in conversation:

• 운전하느라(고요). / 운전하느라고요. (…I was driving.)
  Tone supplies the apology.