Will the list owner see if I mark an item reserved or purchased?
No. List owners will not see which items you marked reserved or purchased on their My List view of lists, but others shopping the list will (to prevent duplicates). Your gift choice remains a surprise for the list owner.
Note: The list owner can create lists under child accounts, and those we
do show the status to the list owner, since they are managing these lists, often for kids. The list owner would be able to see that grandparents or aunts and uncles have purchased something off those lists. But, for example, if you mark something as purchased on your cousin's list, your cousin won't see it and know that you bought it. You can tell if a list is a child account – the member name is indented below the parent of the account.