Finally, I have found source of the problem and want to share it for others, having the same problem.
It turned out, that I accidentally unchecked Treat as an alias checkbox for my main account, on Settings → Accounts and Import → [account name] → edit info. After checking it back (this time for all my accounts) entire Reply functionality got back to normal.
Turns out, that this is not a bug, but some kind of feature, about which Google is aware and have it described in details. Most important parts:
If you use Gmail's Send mail as feature to send messages on behalf of another email account, you may encounter the following issues: (...) If you receive a message from a Send mail as address and you click Reply, the To: field is incorrectly populated with your primary address. (...) These issues occur because Gmail treats your Send mail as address as an alias of your primary address. You can change this behavior in your mail settings by deselecting Treat as an alias.
And now, comes the best part. Either I'm missing something, or in my case the solution was to do something exactly opposite to what Google suggests! From my understanding of above text (correct me, if I'm wrong), I should deselect Treat as an alias to fix the problem, that To: field is being incorrectly populated with my primary address (that is exactly, what was happening to me).
Well, the problem is, that I was experiencing above mentioned problems when I had Treat as an alias checkbox unselected. And selecting it back solved the problem. Only after then my To: field started to become correctly populated—exactly how it is described in Kevan Sheridan's answer.
Clearly there is no daily quota - unless my experience is untypical. It can be months before even a single one of my Gmail items is sent to Spam. I have been careful about disclosure of my Gmail address (I use an address at a different service provider when obliged to provide such a means of contact to those I do not fully trust. I have even set up a temporary account at a third service provider for a contact I did not trust at all.)
As you mention, the general public does not know all the details of how Gmail decides what to treat as spam. What we do know, or can predict with reasonable certainty, is that a lot of the factors taken into consideration are to do with the message itself or the sender - not the recipient. For example blacklists of sources, content analysis (including Subject, other 'header' details, multiple addressees), frequency of submissions and spam reports.
A recipient can do little to affect this other than to report as spam (no use to you when you want less aggressive treatment) or, probably, to delete without opening the mail.
So I suggest you either "Mark as read" before deletion, or you open emails before deleting those from people you do not want to be treated as potential sources of spam. Moving them (even if unread) to a folder (other than Spam!) prior to deletion might help.
Best Answer
You can use vacation responder for this.
Go into your Gmail settings and looks for a section called "Vacation Responder"
This will allow you to enter an auto-response for all incoming messages. Just uncheck the "Ends" box to make sure it will always be on.
Note: like it says in the help text in the image, if a contact sends you several messages, this automated reply will be sent at most once every 4 days.