Greetings, welcome to Amharic wikipedia. For the terms you requested I would go with:
One-party state/ One party country: አንድ ፓርቲ አገር Dictatorship/whatever is North Korea: አምባ ገነንነት Monarchy: ንጉሳዊ አገዛዝ Constitutional monarchy: ንጉሳዊ አገዛዝ Republic: ሪፐብሊክ Islamic republic : እስላማዊ ሪፐብሊክ Parlimentary Democracy: ፓርለሜንታዊ ዴሞክራሲ Constitutional republic: ሪፐብሊክ Unitary presidential constitutional republic? ፕሬዚዳንታዊ ሪፐብሊክ?
I have omitted 'constitutional' since every country today has a constitution, so all monarchies or republics can be called constitutional.