1. I shall be lonely with you away.
2. I shall be lonely if you are away.
(Does #1 mean #2 in meaning?)
3. She smiled brightly, extending her hand.
4. She smiled brightly while she extended her hand.
5. She smiled brightly and she extended her hand.
6. She smiled brightly and she extended her hand at the same time.
(Are the four sentences all grammaticall? In #5, did the two actions happen at the same time or not? Does #5 mean #6?)
Yes, 1 and 2 mean approximately the same thing.
3 - 6 mean the same thing, yes, and there are two actions happening at the same time. Sentence 6, however, is wordy. You don't need the words "at the same time." The meaning is clear without them.