[Coldsaturn]

Yes, so basically, most of the shards you'll get are from the galaxy, but you can occasionally get them from generic wish pulls as well.
10/X means that you're getting pieces of a card you don't have yet. Get all the shards for it to become a fully formed 4 or 5 star memory.
Whole number (not a fraction) means that you already own that card, and those additional shards you're collecting can be used to rank it up. 3 star cards need 20 shards to rank up, 4 star cards need 30, and 5 star cards need 40.

You can't buy shards, if you tap on each of those it will either direct you to the Wish pull page or the galaxy explorer. The only exception is for cards available in the Wishing Well Exchange. This is that shop sub menu where you can buy cards using blue gems (you get 1 blue gem for each card you pull from the wish page). You can buy 5 star cards with 180 blue gems, and 4 star cards with 45. It's advised to only buy 5 star cards, because the others at some point will drop in your lap and you'll be able to rank them.

P.S. The wishing well exchange has permanent cards and rotating cards. For the rotating ones choose wisely rather than spending gems for a card that you need less (the choice might be brought by: I don't have x color card and I need it for battles; the card arriving next month is spicier than the one available now; I vibe with it more; etc.)

The rotation is (getting the info from reddit):

January/April/July/October

Original trio - lunar secondary, New boys - primary

Xavier - Fragment Of Time (yellow)
Zayne - Cozy Afternoon (red)
Rafayel - Before Sunrise (pink)
Sylus - Within Reach (pink)
Caleb - Exclusive Aftertaste (red)

February/May/August/November

Original trio - lunar primary, Sylus - tertiary, Caleb - secondary

Xavier - Fluffy Trap (green)
Zayne - Business Trip (blue)
Rafayel - Your Fragrance (purple)
Sylus - Immobilized (blue)
Caleb - Hidden Waves (purple)

March/June/September/December

Original trio - lunar tertiary, Sylus - secondary, Caleb - tertiary

Xavier - Precious Bonfire (red)
Zayne - Gentle Twilight (pink)
Rafayel - Blossoms (yellow)
Sylus - Nightplumes (green)
Caleb - Endless Summer (green)

Advice on which to get: For combat definitely primary and secondary are great to have. Tertiary is nice to have but less important.

Date wise: Spiciest for each guy is their primary card. Secondary for Zayne and Rafayel are also quite intimate but for Xavier and Sylus secondary cards are wholesome. Tertiary cards are in general wholesome and cute with only Sylus having a spicier memory for tertiary. (This is only comparing permanent 5* memories to each other not a general rule).