回复：请求版主单身老猫帮助，关于重婚，找律师。

1：如以重婚及用假身份欺骗起诉他，他是否有很大机会开脱，不需要面对至少1年监禁。（他扬言他会没事

All you can do is to report to a local law enforcement agency. A district attorney will determine whether to prosecute a polygamist. Sentencing is up to a judge.
 

2：如法院核准他重婚，如他真的得以开脱牢狱惩罚，是否仍会有犯罪记录跟随他终身，是否有性犯罪的记录，是否会影响他今后的         工作。

At least in California, polygamy is not a registrable crime under Penal Code 290 (c).
 

3：在起诉他重婚的同时，我是否可要求经济赔偿。

You may. You will need an experienced family law attorney to access your situation and find some creative grounds to sue for damage, such as marriage fraud, breach of contract, misrepresentation, etc.
 

4：我将我和他之间的事实用文字，照片的方式通过邮件公布给他的社交圈是否我会涉及法律责任。

I would advise not to. Depending on what you say, it may cross the line of defamation.
 

5：起诉重婚的刑法律师是否同时帮助我争取抚养权，抚养费及经济赔偿。

No. You will need a family law attorney for custody, support, or any damage you may be entitled.