I use 开门 in phrases such as 还没开门了吗 (háiméi kāiménle ma?), when I want to know if a shop hasn't opened yet, and 你几点开门 (nǐ jīdiǎn kāimén?), which can be used to ask when a shop opens.
I recently encountered 西门开放时间 (xīmén kāifàng shíjiān) on signage, which translates to west gate opening hours, but I don't recall seeing 开放 before this.
Question: What's the difference between 开放 and 开门?