let me answer you question

it's certainly better to start a new H1 with 6 years new period, though you can choose to use up the rest 2 years at your own preference. I am on your LG's situation and just extended another 3 yr. By this way, I have plenty of time preparing for GC application.

Go back to your question, unless he wants to go to industry and use the remaing 2 yrs... while new H1B caps for industry become very exhausted, re-instation a new H1b seems more advantageous.
Tax exemption for H1b holders applies for those who directly arrive in US with H1B, not for F1 students switching to the new H1B. If your LG never used H1B tax exempt, or a J1 tax exempt before, since this time he comes from China, he should be able to entertain some extra money from tax return for 3 yr.

他是在学校工作，因为第一个月的薪水已发，好像是没有扣税，是否是他们搞错了。
No. The school has not done anything wrong. He needs to go to school tax office to fill in a tax treaty and exempt form in order to initialize his tax exempt. Otherwise every month his pay will be deducted certain amount of tax.

To get this extra deduction back from IRS, next year he will need to claim this money back by providing a 1042S form to IRS.
Hope this helps