Answer to first question
If one looks earlier at the beginning of the the creation of the sun and the moon it says (Breishis 1:14-19):
(Source(s) and translation from Sefaria.org)
וַיֹּ֣אמֶר אֱלֹקִים יְהִ֤י מְאֹרֹת֙ בִּרְקִ֣יעַ הַשָּׁמַ֔יִם לְהַבְדִּ֕יל בֵּ֥ין הַיּ֖וֹם וּבֵ֣ין הַלָּ֑יְלָה וְהָי֤וּ לְאֹתֹת֙ וּלְמ֣וֹעֲדִ֔ים וּלְיָמִ֖ים וְשָׁנִֽים׃
G-d said, “Let there be lights in the expanse of the sky to separate day from night; they shall serve as signs for the set times—the days and the years;
וְהָי֤וּ לִמְאוֹרֹת֙ בִּרְקִ֣יעַ הַשָּׁמַ֔יִם לְהָאִ֖יר עַל־הָאָ֑רֶץ וַֽיְהִי־כֵֽן׃
and they serve as lights in the expanse of the sky to shine upon the earth.” And it was so.
וַיַּ֣עַשׂ אֱלֹקִים אֶת־שְׁנֵ֥י הַמְּאֹרֹ֖ת הַגְּדֹלִ֑ים אֶת־הַמָּא֤וֹר הַגָּדֹל֙ לְמֶמְשֶׁ֣לֶת הַיּ֔וֹם וְאֶת־הַמָּא֤וֹר הַקָּטֹן֙ לְמֶמְשֶׁ֣לֶת הַלַּ֔יְלָה וְאֵ֖ת הַכּוֹכָבִֽים׃
God made the two great lights, the greater light to dominate the day and the lesser light to dominate the night, and the stars.
וַיִּתֵּ֥ן אֹתָ֛ם אֱלֹהִ֖ים בִּרְקִ֣יעַ הַשָּׁמָ֑יִם לְהָאִ֖יר עַל־הָאָֽרֶץ׃
And G-d set them in the expanse of the sky to shine upon the earth,
וְלִמְשֹׁל֙ בַּיּ֣וֹם וּבַלַּ֔יְלָה וּֽלֲהַבְדִּ֔יל בֵּ֥ין הָא֖וֹר וּבֵ֣ין הַחֹ֑שֶׁךְ וַיַּ֥רְא אֱלֹקִים כִּי־טֽוֹב׃
and to dominate the day and the night, and to separate light from darkness. And G-d saw that this was good.
וַֽיְהִי־עֶ֥רֶב וַֽיְהִי־בֹ֖קֶר י֥וֹם רְבִיעִֽי׃
And there was evening and there was morning, a fourth day.
Based on what it says in 1:18, the verse seems to be speaking in terms of their respective ruler-ships as defined in 1:16 i.e "the greater light to dominate by day (i.e. the sun) and the lesser light to dominate at night (i.e the moon)"
Answer to second question.
The Ibn Ezra on 1:18 says the following.
ולמשול. יום התורה משעת צאת השמש עד בואה והלילה מעת ראות הכוכבים וצדקו האומרים ע''פ שלשה עדי' ודע כי עת שתחשך השמש יהיה ערב עד שעה ושליש שעה שיראה כמו אור בעבים וכן הבקר אור קודם זריחת השמש ובצאת אור השמש ביום ואור הלבנה בלילה יבדילו בין האור ובין החשך
"and to dominate" - the day of the Torah is from the hour that the sun rises until its setting, and the night is from the time of seeing the stars, and they were correct who said: at the word of three witnesses. Know, that the time that the sun become darkened is evening, [continuing] until one and a third hours, when a semblance of light can be seen in the clouds, and likewise morning - light before the [actual] shining of the sun. With the emergence of the light of the sun in the day and the light of the moon at night, [people] will distinguish between light and darkness.
Hope this is helpful.