I have bought a second hand acoustic guitar. The nut with the slots for strings is showing in the following picture. The slots are very deep. It looks weird. Should I file the nut to make it lower? Is there a standard slot depth for acoustic guitars? How about for classical guitars? I have search in this forum and found no information. I am a beginner, any help will be highly appreciated. Thank you.
Weird? What's weird about it? The height of the top of the nut really has no bearing on anything except aesthetics. And that doesn't look too bad. Perhaps a previous player has deepened the slots to make it easier to fret at that end of the fingerboard.
As long as the strings don't rattle or buzz on the lower few frets, it'll be fine. If you really want to file some off the top, do so, but the majority of us would rather spend that time playing the guitar.
Having a low action at the nut is important on a (steel string, non-classical) acoustic guitar, because the string tension is higher than on a classical guitar, making barre chords etc harder. Of course you don't want the action so low that it causes string buzzes, but you say
Fortunately, no buzz on the lower few frets.
Taking that into consideration, my reaction on seeing your guitar is: I'm jealous that you got a guitar that someone took the time to set up properly! Many acoustic guitars are sold with a ridiculously high action at the nut and really needing a proper set-up, including a nut filing.
I'd also think that filing down the top is likely to make the nut look worse. If you really don't like the look, you might consider getting a new nut and filing down the base of the nut to achieve more-or-less the right action, then filing the slots just where necessary to get each string exactly right (or getting a good guitar tech to do it for you). But honestly, things like nut and saddle height are all about getting the instrument to play right.