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?
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.