Why did he attribute the warning not to harm Yaakov to "the G-d of your father" and not to the G-d of Yaakov himself?
Seforno: Because he did not consider Yaakov sufficiently worthy of Hashem appearing to him on his own merit, since he had stolen his heart and fled without informing him.
Why is Lavan telling Yaakov that Hashem told him not to harm him?
Bechor Shor, Malbim: He shows him that he did foolishly. I have power to harm you. This is why Hashem needed to warn me not to!
Oznayim la'Torah #1: Perhaps this was part of Hashem's command "Leimor;" Lavan was forced to tell this to Yaakov.
Oznayim la'Torah #2: In order to boast that Hashem had appeared to him.
Who did Lavan mean that he has power to harm them?
Tosfos ha'Shalem (3, citing R. Efrayim): He could harm Yaakov and his slaves. He would not harm his own daughters and grandchildren. Ha'amek Davar - "Avichem" (plural) refers to Yaakov and his slaves, who served Hashem. Avraham and Yitzchak are the father of all of them. Even though his gripes were only against Yaakov, when Nochrim see a Yisrael steal, they say that all Ovdei Hashem are thieves, and do evil to all of them. He thought that Judaism corrupted them, so he must uproot this from them. This was a Siman for generations.
Oznayim la'Torah: He was referring to all those mentioned in the previous Pasuk - Yaakov, his sons and is wives. 1
Oznayim la'Torah: A clear indication that he intended to destroy everything - as we say in the Hagadah, 'Bikesh Lavan La'akor Es ha'Kol.'
Hashem told Lavan "Pen Tedaber." Why did Lavan say "Hishamer Lecha mi'Daber"?
Ha'amek Davar: He lied, to 'prove' that he could ignore Hashem's warning and harm him, just he does not want to. Hashem told me not to speak to you at all, and I am speaking! (Really, Hashem warned him only not to speak bad, but he was permitted to speak good.) I do not fear those who serve your fathers' G-d. I could wipe you out! Amidst my virtue, I request only my gods. He thought that Yaakov took them to stop Lavan from idolatry, or to disgrace them. Really, he did fear Hashem's warning. He wanted to uproot everything (like we say in the Hagadah), i.e. to kill Yaakov and take his grandchildren, and uproot them from Torah.