(a) It is the first time that we have met.
(b) That was the first time that she had traveled alone.
(c) Yesterday was the first time that Ted swam in the Atlantic Ocean.
In the sentences above,
Q1) Can we change the bold 'that' into 'when'?(in terms of grammaticality)
Q2) Can we change the bold 'that' into 'in which' or 'at which'?(in terms of grammaticality)
Q3) What is the bold 'that' called in grammatical terms? I am curious about its grammatical identity. Is it a 'relativiser' or a content-clause-introducing 'complementiser'(e.g. in 'the fact that I ran away') or anything else? (I know that in this construction, 'that' or 'null' is common. What I wonder about is the grammatical origin or identity, of 'that'.)
Actually, I have consulted many sites as best I can. But I couldn't draw an overall conclusion because there are two conflicting opinions.
https://english.stackexchange....a-is-the-that-clause (especially, Mr. Lawler says a relative pronoun 'when' can be used even though the use is limited to specific circumstances)
And when I searched COCA, there is 7 results of 'the first time in which' and 11 results of 'was the first time when'.
I appreciate your teaching in advance.