In a sentence:
I went to New York, too.
q1:
What was presupposed the thought of the speaker?
1) I went to Boston.
2) He went to New York.
a1:
What do you mean about 1. and 2 ? This is a speaker thought sequence ?
Speaker 2 states this “I went to New York, too”.
That implies that at some point in the conversation before, speaker 1 stated that he has visited New York, and speaker 2 stated that they have been to New York as well.
So its more like
1) I went to New York
2) I went to New York, too.
q2:
Is this "too" replaceable with "as well?"
a2:
You mean the “too” in “I went to New York, too.”
Yes, you are correct. This has the same meaning as saying “I went to New York, as well.”