1. I will go abroad.
2. I would go abroad.
3. I will prefer an aisle seat.
4. I would prefer an aisle seat.
5. I will do it.
6. I would do it.
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Q1: Are they all grammatical?
Q2: What is the difference between 'will' and 'would'? If we use 'would,' can we use the sentence politely?
1, 2, 4, 5, and 6 are fine. In 3, the word "will" is not needed.
Generally, "will" is used to indicate future actions, and "would" is used to indicate future possibilities. Here's more information about these two:
http://grammar.ccc.commnet.edu/grammar/auxiliary.htm#would