I want to make a homebrew warlock subclass, but only a small amount of the spells I try to add to the spell list are available because I don't have the book. Is there anywhere where all the free spells are displayed? (I'm new to dnd and even newer to homebrew)

Right here:

https://www.dndbeyond.com/spells?filter-class=0&filter-search=&filter-verbal=&filter-somatic=&filter-material=&filter-concentration=&filter-ritual=&filter-sub-class=&filter-source=1&filter-source=4

I hope that helps.

https://www.dndbeyond.com/spells?filter-class=0&filter-source=1&filter-source=4&filter-source=29

Quote from Mairondil >>

https://www.dndbeyond.com/spells?filter-class=0&filter-source=1&filter-source=4&filter-source=29

 Your list includes UA spells which cannot be added to a homebrew and still be published.

Quote from IamSposta >>

Quote from Mairondil >>

https://www.dndbeyond.com/spells?filter-class=0&filter-source=1&filter-source=4&filter-source=29

 Your list includes UA spells which cannot be added to a homebrew and still be published.

 True. Your link if OP wants to publish the subclass. My link if OP just wants to use it for themselves.

Thanks this helps heaps!