First, realize that some people actively process information through discussing and talking through it. You presumably are not in this group, but some people are. In a generalized sense, this is an introvert vs extrovert processing situation.
My experience as an introverted processor - I cannot follow a fast moving, unguided conversation at all - is that most people who can do this are completely and utterly oblivious to the fact that others want a structured, defined, organized conversation, and are completely lost without it.
Second, the problem you are describing is not ever fully resolvable without a defined plan. There always will be things lost in those short conversations, even for people who are "good" at processing information verbally.
My recommendations are to address both pieces of this - meetings as well as drop by requests.
- Have a meeting agenda and shared document to edit/create. Having a meeting agenda helps you be prepared for the discussion. Having a spec/doc that is updated realtime helps everyone to confirm and finalize the discussion
- It is probably a good idea to also have meeting notes which get sent out after a meeting capturing any decisions regardless, too
- I've found having meeting notes be updated as part of the meeting to be hugely beneficial, particularly when combined with an agenda
- Request updates in writing. This is simple to do and something I (and nearly everyone else in technical fields) end up doing. It's just too easy to have things lost in translation. After talking about it, just ask, "can you confirm what you are asking in email/request/etc form so I can make sure I didn't misunderstand?"
- You may have a formalized system for this or not, but even an email can be beneficial
- Probably best to have a formalized system though, as much as people hate them issue trackers such as jira/redmine/etc solve this problem well. I'm not familiar with YouTrack but it appears to be good for this, you may want to create tickets for people as Dan Lyons suggests
These two suggestions should solve most of your issues.
I have similar, though perhaps not as extreme, issues as you do and on at least one project I've worked on with people who love verbal processing would have been completely lost without the above. I could not follow meetings at all and was overwhelmed in the "minor spec" requests. In my case I just used a shared OneNote workbook - but it was a small enough team this worked.