If I get several of my answers down voted, will I be allowed to post answers further? Will I be blocked from the community? Please mention if the rule is applicable for all stack exchange sites?
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Yes, given too many poorly received prior answers, it is possible to get (automatically and for some time) banned from answering questions. This affects only the ability to answer; the account will not be suspended.
This is the case on all sites. Yet, it is determined on a per-site basis; a ban on one site does not result in a ban throughout the network.
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6$\begingroup$ Relevant links: Why are answers no longer being accepted from my account? (from the Help Center) and What can I do when getting “We are no longer accepting questions/answers from this account”? (from Meta Stack Exchange). $\endgroup$ – user642796 Jul 10 '17 at 18:12