Jacob's claim that God answered him (Gen 35:3) could reasonably refer to the actual oath Jacob made (interpreted as a prayer-oath) when naming the place Beth-El. It, however, is unreasonable to interpret the Vision of God as a response to a prayer since Gen. 28:16 states
Jacob awoke from his sleep and said: "Indeed, God's presence is in
this place and I didn't know it.
Jacob was surprised. This clearly shows that God did initiate the Vision. However verses 18-22 read as follows:
Jacob awoke in the morning; he took the stone on which he rested his
head and made it a monument; he poured oil on its head. And Jacob
named the place Beth-El (literally, House of God), even though
originally its name was Luz.
And Jacob vowed a vow as follows:
If God will be with me, watch me on the path I am going, give me food
to eat and garb to wear, I return safely to my father's household, and
God will be my Lord, then this stone which I have made a monument will
be a House of God, and of all You give me I will give a tenth to you.
I think it plausible to regard this as a coupled prayer-vow. Jacob is praying for safety, food, garb, and a peaceful return and in exchange for God being Jacob's Lord (constantly watching and providing) Jacob vows to make Beth-El a house of God and to give tithes.
It is pretty explicit that Jacob alludes to this vow-prayer in Gen 31:7-13.
And your father (speaking to his wife) belittled me and changed my
wages 10 fold but God did not allow him to harm me.....God appeared to
me in visions [when Laban attempted to change wages]...God say "I am
the Almighty of Beth-El where you anointed a monument and made a vow.
As to the grammar of "answer" I would note that the present conjugation is used
To the God who answers me on the day of my problems and who was with
me on the path I went.
Building on Wenham's observations, we see two verbs in this sentence. Answer is conjugated in the present while "who was with me" is conjugated in the past.
I think it reasonable (and consistent with the English translation ) to interpret this as a habitual present, "God who answers me whenever I have a problem." There is no standard way to indicate the habitual present in biblical Hebrew and it can be indicated by a future, past, or present conjugation so this is a reasonable approach