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I assume that my posts are deleted when I delete my Facebook account, but what about the "like"s that I gave to other posts? Is the "likes" count on that post/page reduced?
Or the comments I made on other posts? Are they deleted?
And what happens to the conversations I had in chat?
Do they still appear to the people I chatted with?
If you deactivate your account, all your comments, likes, shares, post and everything associated with your profile disappears like it never existed. But your message conversation will still be visible on your friend's inbox just there won't be your profile picture and link to it.
If you reactivate the account in future all your likes, comments etc. will reappear.
If you choose to permanently delete your Facebook profile, the same thing happens plus all your data from facebook servers will be erased permanently, so there's no way you can regain access to your account as well as the data associated with it.
If you want you can download all your data from Facebook before deleting the account. Goto your account settings https://www.facebook.com/settings and click on the link that says "Download a copy of your Facebook data" and download the archive.
Your activities are indeed not visible anymore to other users. However, Facebook does not nessesarily delete them. In many cases, they only mark it as deleted and make it invisible to you (and others).
Source: http://www.europe-v-facebook.org/EN/Data_Pool/data_pool.html
On scrolling down (f.e. to "Satus Updates" at the end), you can see, that these are not deleted.
Yes, the likes and comments are deleted after you deactivate you Facebook profile, like they were never there.
But the chat remains there. You even remain in your friends’ lists of friends but with no profile picture and no link to you account. Here is the screenshot of messages in your friends’ inbox after you deactivate you account:
