Two Questions!

1st Question: How should I be spending my pearls? I'm currently F2P and I have amassed around 1000 pearls. I have also never spent pearls on anything other than a few inventory upgrades.

2nd Question: How do I get duplicate parts to evolve, is it just RNG?

 

Well there's not many options,

you can spend pearls on sugar/gold - not recommended for f2p
you can spend it on shop refreshes - not recommended for f2p

inventory slots - debatable
you can spend it on crew so you can get your second tier ship faster - debatable
you can spend it on the epic chest for a potential item you can work on - debatable
you can save it for the 10 epic chest - debatable

if you favor long term then obviously the 10 epic chest will be the way to go

if you want a smoother beginning then getting your second tier ship or higher grade equip would be the other option



for your second question, its rng

 

Idd just keep saving them if I were you there's nothing you really need with pearls at this point
And it's just random!

 

Inventory slots do become rather important... But I agree that if you are F2P then mostly saving for the 3900pearl box is a great option. Everything can be earned by grinding at the game, EXCEPT for inventory slots... But the big box does give a nice boost to the items you have available and gives a good chance to get a duplicate item you've been waiting for