Should I Mine Glommer's Statue?

Mining the statue does not completely destroy it. On a full moon, a Glommer's Flower will spawn at the base of Glommer's Statue (even if it has been mined). Picking up Glommer's Flower will trigger Glommer to become a permanent "follower" (until Glommer dies).

What do I do with Glommer's flower?

When a Glommer connected to a flower dies, the flower converts into a perishable item which spoils after 6 days. In this state, it can be used as fuel for fires or the Ice Flingomatic. A perishable flower can still be used to craft an Old Bell.

What do I do with Maxwell statue?

If the player destroys the Maxwell Statue that is present in the final chapter of Adventure Mode (Epilogue: Checkmate), 3-4 Clockwork Monsters will spawn around the statue, and the player's sanity level will drop to 0 immediately. The player must kill all the mobs to restore sanity.