If I amend my claims after normal publication (18 months), I believe my application will get republished again with amended claims.
How long that process would take?
Your application will NOT be republished. The amended claims will be added to the applications file history (called the 'Image File Wrapper' in both Public PAIR and Private PAIR), almost always the same day as they are received. The amended claims are view-able as submitted, and are not incorporated into the body of the application in any way.
The Patent Office will also publish the application with all of the amendments in its final form once the application issues into a Granted Patent.
However, if you would really like to republish an application before Issuance, according to MPEP 1130(I) the Patent Office will republish amended applications if you request it along with: