Yes, ゆうがたGet! (Yuugata Get!, Evening Get!) is a real-life TV show.

It's broadcasted by TV. Shinshu located in Nagano prefecture since April 5, 1999. Based on the broadcast schedule list on the Wikipedia, the show started at 4:30 on the weekdays in:

• April 1999 - September 2000 under the name of 「陽司★美恵子 ゆうがたGet!」, and
• March 2010 - March 2014 under the name of 「情報ワイド ゆうがたGet!」

As already mentioned on the question, Ryuta Mine is also a real-life person. Based on the list of appearance on the Wikipedia, he appeared once every month on Wednesday in:

• 「情報ワイド ゆうがたGet!」, and
• 「ゆうがたGet!」

which means the story took place in between 2010-2014 instead of 1999-2000.

Regarding the episode of Mino Monta's son, I couldn't find the specific date/episode. but it's probably regarding

 

_{Wikipedia - Monta Mino}

Considering the publication month of chapter 5, the episode (if it existed) should be broadcasted before August 2012.

_{P.S. it might be possible that the author took the events that had occurred recently at that time since the manga was serialized in 2012-2015.}

Yes, ゆうがたGet! (Yuugata Get!, Evening Get!) is a real-life TV show.

It's broadcasted by TV. Shinshu located in Nagano prefecture since April 5, 1999. Based on the broadcast schedule list on the Wikipedia, the show started at 4:30 on the weekdays in:

• April 1999 - September 2000 under the name of 「陽司★美恵子 ゆうがたGet!」, and
• March 2010 - March 2014 under the name of 「情報ワイド ゆうがたGet!」

As already mentioned on the question, Ryuta Mine is also a real-life person. Based on the list of appearance on the Wikipedia, he appeared once every month on Wednesday in:

• 「情報ワイド ゆうがたGet!」, and
• 「ゆうがたGet!」

which means the story took place in between 2010-2014 instead of 1999-2000.

Regarding the episode of Mino Monta's son, I couldn't find the specific date/episode. but it's probably regarding

the arrest on 13 September [2013] of his 31-year-old son, Yuto Minorikawa (御法川 雄斗), who was charged with stealing a man's bag on the street in Tokyo.

_{Wikipedia - Monta Mino}

Considering the publication month of chapter 5, the episode (if it existed) should be broadcasted before August 2012.

_{P.S. it might be possible that the author took the events that had occurred recently at that time since the manga was serialized in 2012-2015.}

Yes, ゆうがたGet! (Yuugata Get!, Evening Get!) is a real-life TV show.

It's broadcasted by TV. Shinshu located in Nagano prefecture since April 5, 1999. Based on the broadcast schedule list on the Wikipedia, the show started at 4:30 on the weekdays in:

• April 1999 - September 2000 under the name of 「陽司★美恵子 ゆうがたGet!」, and
• March 2010 - March 2014 under the name of 「情報ワイド ゆうがたGet!」

As already mentioned on the question, Ryuta Mine is also a real-life person. Based on the list of appearance on the Wikipedia, he appeared once every month on Wednesday in:

• 「情報ワイド ゆうがたGet!」, and
• 「ゆうがたGet!」

which means the story took place in between 2010-2014 instead of 1999-2000.

Regarding the episode of Mino Monta's son, I couldn't find the specific date/episode, but it's probably regarding

the arrest on 13 September [2013] of his 31-year-old son, Yuto Minorikawa (御法川 雄斗), who was charged with stealing a man's bag on the street in Tokyo.

_{Wikipedia - Monta Mino}

which subsequently narrows the setting to the year 2013.

_{P.S. it might be possible that the author took the events that had occurred recently at that time since the manga was serialized in 2012-2015.}

Yes, ゆうがたGet! (Yuugata Get!, Evening Get!) is a real-life TV show.

It's broadcasted by TV. Shinshu located in Nagano prefecture since April 5, 1999. Based on the broadcast schedule list on the Wikipedia, the show started at 4:30 on the weekdays in:

• April 1999 - September 2000 under the name of 「陽司★美恵子 ゆうがたGet!」, and
• March 2010 - March 2014 under the name of 「情報ワイド ゆうがたGet!」

As already mentioned on the question, Ryuta Mine is also a real-life person. Based on the list of appearance on the Wikipedia, he appeared once every month on Wednesday in:

• 「情報ワイド ゆうがたGet!」, and
• 「ゆうがたGet!」

which means the story took place in between 2010-2014 instead of 1999-2000.

Regarding the episode of Mino Monta's son, I couldn't find the specific date/episode. but it's probably regarding

_{Wikipedia - Monta Mino}

Considering the publication month of chapter 5, the episode (if it existed) should be broadcasted before August 2012.

_{P.S. it might be possible that the author took the events that had occurred recently at that time since the manga was serialized in 2012-2015.}