What is the meaning of "[Ki Zansah Imam] Hovishah Horosam"?
Rashi, based on Targum Yonasan: The Chachamim who give rulings for them, they are ashamed due to Amei ha'Aretz. [The Chachamim] say 'do not steal', and they steal; 'do not lend with Ribis', and they lend with Ribis.
Radak citing Targum Yonasan: Your Kenesiyah strayed after the false Nevi'im; their teachers are ashamed.
Malbim: The children are Bnei Zenunim. We say that a married woman, most of her Bi'os are with her husband, so we attribute her children to him, and they are Kesherim. However, this is only if she is Mezanah covertly; she is in his Reshus and fed on his table. If she publicized her Zenus, and said "Elechah Acharei Me'ahavai" and left his Reshus to the Reshus of Zonim, most of her Bi'os are with adulterers. And especially here, that she admitted that she is not fed from her husband, rather, from the adulterers, who give "Lachmi u'Meimai", and wool and linen for her to make her garments, and other needs, i.e. oil to anoint and drinks for pleasure, e.g. wine and milk, her children are from Zenus.
Malbim (according to the Nimshal): The Kenesiyah totally separated from Hashem. She openly serves idolatry. She thinks that all her abundance and success are due to the Ma'arachah (stars and Mazalos), and Hashem will not benefit or harm; there is no benefit to serving Him at all. She will be like all families of the land, to serve wood and stones. Therefore, Hashem will not have mercy on the good ones, and will cast all away from His face.
What is "Elecha Acharei Me'ahavai"?
Rashi: These are the ways of Nochrim.
Radak: Her lovers are Ashur and Egypt. Yisrael had a Bris with them, and they saved them from their enemies. Yisrael were confident due to the bribes that they gave to them. Since Yisrael had Shalom via their Bris with Ashur and Egypt, it is as if those nations supplied Yisrael's needs. With their help, Yisrael were able to work their land and go from land to land in Shalom. It is considered that they gave "my bread, water, wool, linen, oil and drinks." She should be ashamed of her deeds, and trusting in her lovers, for they will not help her at the time of her affliction.
Radak citing his father: Her lovers are the sun, moon and stars, which she served. They thought that the sun, moon and stars supply their food and needs ? "u'Min Az Chadalnu Lekater li'Mleches ha'Shamayim v'Hasech Lah Nesachim Chasarnu Chol uva'Cherev uva'Ra'av Tamnu" (Yirmeyah 44:18).
What are "Shikuyai"?
Radak: Wine and other drinks.