some questions before applying for postdoc I appreciate your guidance on the following questions:


Should I inform my adviser before applying for each an every postdoc position? 
Should I send my research statement to my Ph.D adviser before sending it for postdoc applications?
In general, you should be communicative with your PhD advisor about your applications. This is so that they can do their job and advise you about the process. Their input will be invaluable to you. In particular, you will probably want your PhD advisor to write recommendation letters for you. 

You should tell your advisor in advance that you are planning to apply. (Although it is usually not necessary to specify exactly where.) And, once you have applied, you should tell them where so that they are on the look out for a letter request.

However, if you have a problematic relationship with your advisor, then that's a big problem that you will need to navigate. If this is the case, then your question should make this clear.