I found this definition for rise in LDOCE:
3 stand: formal to stand up:
Then she picked up her bag and rose to leave.rise from the table/your chair etc
The chairman rose from his chair and came forward to greet her.
He put down his glass and rose to his feet.
This suggests that "from" is the preposition of "rise." Then why "in" has been used?
Hagrid helped Harry on to the train that would take him back to the
Dursleys, then handed him an envelope.
"Yer ticket fer Hogwarts, " he said. "First o' September — King's Cross
— it's all on yer ticket. Any problems with the Dursleys, send me a
letter with yer owl, she'll know where to find me…. See yeh soon,
Harry."
The train pulled out of the station. Harry wanted to watch Hagrid until
he was out of sight; he rose in his seat and pressed his nose against
the window, but he blinked and Hagrid had gone.
and one more question: Would it be wrong to use "onto" instead of "on to" in the bold sentence? What would the difference be in meaning and grammar?
Best Answer
Because he didn't stand up: he didn't rise from (out of) his seat, he raised his body a little bit while still in his seat. He "moved from a lower position to a higher one" while still in his seat.
rise
(Oxford)
To be 'in' his seat means to be 'enclosed' within his seat; so one can rise in one's seat by raising or boosting oneself up by several means. One's bottomside does not have to be in contact with the seat bottom to be considered in one's seat. Etiquette might say that, but grammar doesn't
I believe the difference between onto/on to and/or into/in to has been covered previously; search for it and if you can't find an answer, ask a new question.