Advise needed for a newbie

I just got my hands on a small garden! But I have no idea where to start…

There are quite some plants already planted: an olive tree, some small palm trees (that I don’t like), a Japanese maple (?), a raspberry bush and some others I don’t recognize (mostly decorative). Most of the floor is lawn (that I am letting grow wilder). Unfortunately I am not able to include a photo, it’s not loading.

I am in a 9a/9b zone (I think: mild winters rarely if ever freezing, mild summers, quite wet the whole year, continental Europe).

My questions:

• what can I do to maintain the lawn walkable but let it get more diverse?
• what tools do I need for every-day maintenance of a small garden?
• do you have any advice on plants both perennial and annual for newbies? I’m in particular interested in small plants that produce something edible. Ideally would like to start with a small apple tree? And a pumpkin/zucchini plant next year?