Your friend’s grandma seems pretty cool.

I’m going to guess most of not all were purchased at some gift shop while she was on vacation based on the pin that says Moscow Treasures, and the fact that one of the pins belongs to an Italian soccer team.

red star with the flag is for the red army guard units, units that were awarded an “elite” status after wartime service. the ones with the red cross/crescent are for people who donated blood in the USSR for the red cross/crescent (there are third and first class pins for it on there). the one with lenin’s head is for “udarniks” (shock workers), highly productive and disciplined laborers. the one with the white circle and red star in the middle is some kind of excellence award for soviet army i believe (directly translating what it says). the normal red star with hammer and sickle pins around the hat are pins that came standard with these kinds of pilotka caps. the one with the 3 is a proficiency badge for soviet enlisted soldiers. the one with the running guy is a military sport/athletics proficiency badge. the large one on the right thats hanging i cant really make out the first two characters but it says MVD, ministry of internal affairs, so maybe that. the one with the 1 on it is probably another athletic proficiency badge, it says “razryad” on it. those are all the ones i can identify, hope this helps. if you want to try and find more of them, this site has a lot of these soviet pins documented.

ударник xii пятилетки 12th five-year plan of the USSR

гвардия - soviet guard https://ru.wikipedia.org/wiki/Советская_гвардия

донор (the one with the red cross) is obvs blood donation https://ru.wikipedia.org/wiki/Почётный_донор_СССР

“Donor of the USSR” was awarded to persons who repeatedly donated blood to save the lives of the sick and injured in the defense of the socialist Fatherland, the protection of the State Border of the USSR and public order, natural disasters and accidents, while simultaneously working to involve the population in the ranks of donors"

bottom right Внутренние войска МВД (вв мвд) Internal troops of the Ministry of Internal Affairs of the USSR https://ru.wikipedia.org/wiki/Внутренние_войска_МВД_СССР

Ударник коммунистического труда https://ar.culture.ru/ru/subject/znachok-udarnik-kommunisticheskogo-truda

1 разряд is first category. it looks like its for javelin throw?

1941-1943 брянск is for Bryansk Front https://ru.wikipedia.org/wiki/Брянский_фронт

I’l try. Left to right, top row:

Half cropped one: 3rd degree of i don’t really know what. Probably from amateur sports event. | Basic red star with hammer and sickle: no idea what they are. | One with the ship: don’t know. | “ударник XII пятилетки”: what it says, yes. Somebody worked their ass off in five-year-plan and got this thing to show for it. | “гвардия”: for service in soviet Red Guards. My granpa had one too. | Modern Russian CoA: no idea. | “I донор СССР”: donor USSR 1st degree. Usually for blood donations. | “1941-1943 брянск”: my grandfather had this one. Got if for beating nazis out of city of Bryansk, but it might be just a commemorative one and given to people who didn’t actually fight there for other reasons. | Blood drop one: you could get pins like this just for blood donations. | “ВВМВД”: i think that stands for “Внутренние Войска Министерства Внутренних Дел”. Internal Forces of Internal Affairs Ministry.

Middle, left-to-right:

Sickle and hammer with wings: i think it just a basic pin from Aeroflot uniform. | French thingy one: don’t know. | “воин-спортсмен I”: from some army sports event? | “III донор СССР”, like the one above, but third degree. | “1 разряд”: another sports degree of… Some sports, i guess. | Backpack dude: no idea, can’t read it in this resolution.

Bottom, l-r: “отличник советской армии”: for exceptional service in the soviet army, of course. My grandfather had a one like that but with a different design for some reason, i think? | 3: absolutely no idea. | “норильск CNC”: no idea what it is and what it has to do with Norilsk. | That huge one: no idea. | “ударник коммунистического труда”: probably related to 4th in first row. | “moscow treasures”: idk. | Next one: “пожарно-технич(еская?) выставка калинин”: firefighting equipment exhibition in Kalinin, apparently.