Do they fit over your ear?
Yeah they're over the ear.
Do they cancel outside noise?
They don't have ANC but the passive noise cancelling just from the nature of the large ear cups and closed back design will block out the vast majority of your day to day background noise, like normal conversation, light traffic, etc.
Do they leak audio outside of the headphones?
You'd have to have a really bad seal with the ear cups and have the music jacked to max to have any serious leakage. They're closed back so they are specifically designed to not intentionally let noise in or out. Under normal circumstances, you're not going to have any issues.
Do they provide a good "neutral" sound, as I've heard in reviews? Basically, do they work well with music and other forms of audio without tweaking the sound too much?
They are pretty flat, in a good way. They have a mild V shape sound profile, which is to be expected for closed back headphones in general and headphones in that price range specifically, but the V is much less pronounced than most of the other options in its bracket.
This is a frequency response graph. Basically, it shows you how the headphones put out different frequencies relatively. This is where my comment of a "V shaped sound profile" comes from. On the extreme far left we have the sub bass, followed by the first peak, which is the bass. It drops into a shallow valley for the mids before peaking again in the treble range. Speaking as an audiophile who listens to music critically, the balance of the bass and mids in the MDR-7506s are fine, good even, however, note that if you're used to a pretty bassy experience, you will find the bass lacking, because they are far more neutral in that area than the majority of consumer headsets. They do give a little too much on the top end, which can be equalized out, but for someone who is not a critical listener, or someone new to the audiophile space like yourself, you're not going to be able to really tell. They will very likely provide the most well balanced sound you've ever experienced from a set of headphones, and as I said, some gentle equalizing can improve it if, on the off chance, it does bother you (it won't). They are very good for basically any application. Like I said, They Just Work™. They are excellent jack-of-all-trades cans.
Are the non-detachable cable and default headphone cups an issue? I've seen people complain about those and suggest other headphones because of it.
The non detachable cable is only an issue if you don't like a non detachable cable. The cable is pretty beefy, and one of the benefits of the model being around for thirty years is that Sony has done a pretty good job of maximizing the lifespan of the cable. It's highly unlikely that normal use is going to break the cable, even with heavy use over years. The build quality is surprisingly good for the price point. The downside is that, if something does happen to the cable, your options are professional repair, DIY repair which involves taking them apart, desoldering the cable, and installing a new one, or replacing them. Again, this is basically a judgement call on your part, but personally I haven't had any issues. It should be noted that another benefit of being a 30 year old model is that there's a ton of cheap replacement parts. If you are halfway decent at soldering, there's an endless supply of cheap aftermarket and OEM parts of something does break.
As for the ear cups, the stock ear cups are pleather, comfort is mid, and they do get warm if you wear them for a while. Personally, I found them too shallow, but I have some pretty big retard ears. Luckily, the ear cups are easy to replace and there are some very nice and inexpensive aftermarket ones which address the core issues. The ones on mine, I just checked, are like a memory gel wrapped in a velour material. They do not get warm over extended listening sessions and are extremely comfortable. Looking around online, you can get ones like this for $20-$30.
Note: I busted out my MDR-7506s for the first time in probably years and listened to a pretty wide variety of media to give you the best impressions I can. I hope these answered your questions. Please don't hesitate if you have any more.
