Why does it say "Chai Ani
Malbim: This was decreed on him with a Shevu'ah.
Why does it say "Kanyahu"?
Radak: It refers to Yehoyachin. He is called Kanyahu to belittle him.
Why does it say "Ven Yehoyakim"?
Malbim: This is why this was decreed on him. Nebuchadnetzar exiled him due to his father's sin 1 .
I.e. because he persisted in his father's sin. Then, Hashem punishes the son for his father's sin (Brachos 7a).
What is "Chosam Al Yad Yemimi"?
Rashi: It is engraved and sealed in the flesh of my arm.
Radak: It is like a signet ring used to sign letters. The same applies to "Simani k'Chosam" (Shir ha'Shirim 8:6), "Chosamcha u'Fesilecha" (Bereishis 38:18). The ring never leaves the man's hand during the day or at night. Therefore, it says that even if Kanyahu would be like a Chosam on My right hand, which never leaves it, from there I will remove you and fix you.
Malbim: It says "on that day I will take you, Zerubavel ben She'alti'el Avdi and I will make you like a signet" (Chagai 2:23). Melech ha'Mashi'ach will be like a Chosam on Hashem's right hand. Just like on a Chosam they engrave the master's name and inform who he is, so through Mashi'ach's deed Hashem's name will be open and His wonders will be known in His world.
What is the meaning of "Etekenka"?
Rashi: This is like "Hatikem k'Tzon l'Tivchah" (12:3, separate them from life to death) and "Ad Hatikenu Osam Min ha'Ir" (Yehoshua 8:6). The Nun is extra.
Rashi citing Shir ha'Shirim Rabah 8:2: In the place she'Natak (to which he was uprooted), Nitkan (he was fixed). He repented (Radak - in jail,) in Bavel. Hashem asked to annul His Shevu'ah "write this man Ariri" (verse 30). Zerubavel was born to him 1 in Bavel. It was said to him via the Navi "on that day I will take you, Zerubavel ben She'alti'el Avdi and I will make you like a signet" (Chagai 2:23), corresponding to what He said to his father 'if [Kanyahu] will be a signet on My right hand
Radak: A son was conceived from him while he was in jail, and his grandson was Zerubavel. (Surely also Rashi means like this. Divrei ha'Yamim I, 3:17 explicitly says that She'alti'el was Yechanyah's son! Zerubavel ruled in Yehudah and sat on David's throne. Also this was unlike the decree; refer to 22:30:4:1. - PF)