What did Chabakuk pray?
Radak: It was like a Shir from Tehilim. (Refer to 3:1:2:3.) It ends "la'Menatze'ach bi'Nginosai" (below, 19). It says here "Selah" (3, 9, 13), which appears in Tanach only here and in Tehilim. The Tefilah is [to lighten] the affliction of Yisrael in this Galus. It tells the wonders and mighty acts that Hashem did for Yisrael from when He redeemed them from Egypt. He prayed, and said prophetically, that so He will do for them in this Galus, and when they leave Galus, and in the war of Gog and Magog.
Radak citing Ibn Ezra: It is about a hunger that will be in the future 1 , for it says "b'Kerev Shanim Chayehu" (2), i.e. amidst the years of hunger. Also, "ha'Vinharim Charah Hashem" (8) refers to withholding of rain; "Se'or Kashtecha" (9) refers to a rainbow seen in a cloud on a rainy day. "Ki Sirkav Al Susecha" (8) means on clouds, and so it says "Ki Se'enah Lo Sifrach" (17).
Malbim: There are three parts to this Tefilah. (a) Until "mi'Har Paran Selah" (3) is about Galus ? Hashem should not hide His face from His nation. (b) From "Kisah Shamayim" (3) until verse 13 is about Hashem's conduct during Galus, and His revelation at the time of Ge'ulah, when He will save His nation. (c) From verse 14 until the end, he prays for when Yisrael will be plundered and the birth-pangs of Mashi'ach, and informs that they will be a sign of the Ge'ulah.
What are "Shigyonos"?
Targum Yonasan: If Resha'im will repent with a full heart, they will be pardoned. All their sins in front of Him will be like Shogeg.
Rashi: Chabakuk requested mercy for himself for his words above, e.g. "Al Ken Tafug Torah", "va'Ta'aseh Adam ki'Dgei ha'Yam" (1:4, 14) ? he complained about Midas ha'Din.
Radak: This is like "Shigayon l'David" (Tehilim 7:1), a Shir.
