1)
What is "[va'Evkeh] ba'Tzom Nafshi"?
1.
Rashi: It is my fast.
2.
Radak: The prefix Vov is omitted, like "Shemesh Yare'ach" (Chabakuk 3:11). It is as if it says va'Evkeh uva'Tzom Nafshi. This is like "Te'anu Es Nafshoseichem" (Vayikra 16:29). I.e. I constantly cry and fast.
2)
What is shameful for him?
1.
Rashi: They mock me for crying and fasting in front of You.
2.
Radak #1: You are a source of shame; they revile me due to You.
3.
Radak #2: The Notzerim revile me due to the true Emunah that I persist in; I do not accept their Emunah.
4.
Malbim: When I cry to pray for this 1 .
1
I.e. Mezid sinners who revile You (like Malbim said in verse 10 - PF).