Regarding Shout-Out and Scenery Porn — The comparison to Kitakami, Iwate is conicidental; most of the locations are specific places in eastern Shinshu/Nagano, including certain roads (The road along which Kaito first sees Ichika on the train and other scenes with Mt. Asama in the background) and places in Komoro (Tetsurou's apartment building, Komoro-jo—where the gang starts their film by the ruin gate), Japan East Railway Sakudaira Station (where Kaito sees Nanami off in Episode 2), and several well-known places in Karuizawa Shopping District, all shown to be a short distance from Kaito's house. Ep. 11's revelation that his house is '3 hours' by car to Lake Kizaki in Omachi matches this description. Here's some photography of various locations from the show (including the shrine in which they had the test of courage) http://www.cuso4.org/photos/20120526-hnd/20120526-hnd-ntmc.htm
Regarding The Seventies - Not sure it applies. There is little evidence to support this idea; most of the cars do not match the time period (aside from Manami's vintage car everything appears to be present-day within a few years, and the train leaving the station is an E2-series Asama service Shinkansen, which started operation in 1997 at the earliest). The conspicuous lack of cellphones by the characters may simply reflect an editorial/direction decision by the writers to invoke feelings of nostalgia from viewers who are old enough to not have grown up with access to their own cell phones as for granted.
I'm not certain Here We Go Again! fits — my interpretation is that she just settled her affairs with her family and came back after the heat was off. In fact, it's likely that she landed much more safely this time and that was a made up line for the movie.
The Space Federation is a really schizophrenic when it comes to contact policy. They will send a fleet of bots to stop unauthorized interaction with undeveloped planets, but apparently have no preventative measures to stop it, like automatic chart warning activating upon arriving on close proximity on such planet.
Furthermore, Airheads like Ichika are apparently free to get a ship and travel wherever, without any mandatory advising on what you can do and what you cannot do while space-travelling. When her sister comes over she's genuinely surprised to hear that it is against the law to interact with locals.
So either the rules are known to all in federation but Ichika is borderline autistic, or Federation has pretty epic level problems with informing its' citizens of rules and regulations.