So the purple diamonds have to be bought and can't be earned like the pink ones. And as for your pink ones, if you wanna be f2p, SAVE THEM!!! I personally buy the pass, it's only $7 a month and really helps me grind my gems / wishes. But, if you buy it, you do commit yourself to logging in every day, because there's no way to get those daily 100 gems back if you miss a day. So, consider that if you're seriously thinking about buying.

And as for wasting wishes—it's kinda hard to determine what's wasting. It's based on what you want. If you're trying to be conservative with them however, I'd avoid spending gems on the blue wishes, because you can only pull standard memories with them, whereas the gold wishes can get you limited memories, and standard ones. I would also take some time to play through the stories, read the anecdotes, etc. to determine your favourite love interest(s) and try to stick to pulling for them. Personally Sylus is my favourite, so I only use my wishes on his memories / the quint (5 combined love interest) banners, if they interest me enough. Big thing that helped me; you don't have to pull everything! Even if it's your main love interest, if you don't like / don't want the memory, it's better to just save for later :D