Learn Finnish: Päiväkirjassani on lukko.

It is built into the word päiväkirjassani using the possessive suffix -ni. While you could say minun päiväkirjassani, Finnish usually drops the pronoun minun because the suffix -ni already makes it perfectly clear whose it is. Dropping the pronoun is the standard way to use 1st and 2nd person possessive suffixes.

Why does this use the inessive case (-ssa) instead of the adessive (-lla) to say "has"?

Usually, the "have" construction uses the adessive case (like minulla on, meaning "I have"). However, when an inanimate object (like a diary, room, or car) "has" a physical part or feature attached to it, Finnish uses the inessive case (-ssa). Literally, you are saying "In my diary is a lock."

In what order do the suffixes go on the word päiväkirjassani?

The case ending almost always comes before the possessive suffix. Here, the root päiväkirja (diary) takes the inessive ending -ssa (in) first, and then the possessive suffix -ni (my) is added at the very end.

Would it mean the same thing if I changed the word order to Lukko on päiväkirjassani?

Not quite. The word order in Finnish tells us what is new information. Päiväkirjassani on lukko translates to "My diary has a lock," introducing the lock as new information. Lukko on päiväkirjassani translates to "The lock is in my diary," where the lock is already known and you are stating its location.