The Chatter API rate limits are distinct from the overall API call limits, and note that it is scoped to the user:
For applications using a session ID from Salesforce, the rate limit is per user, per hour—there isn't a separate bucket for applications. All applications the user accesses with a session ID use this general quota. To take advantage of the ...
The reason why forceChatter:publisher did not show tab was because i was using it in custom component.
This is an issue in salesforce itself. Here Is the link
@lambad as requested in comment, here is the result of a test to show that the issue cannot be reproduced.
Added simple lightning component (API v.47) into a lightning page called "Custom Chatter Publisher".
Note that forceChatter:publisher is of context="RECORD"
<aura:component implements="flexipage:availableForAllPageTypes,force:hasRecordId" >
Assuming you are using Chatter Questions feature, then editing feed posts (the questions) is not permitted for Community users with some exceptions:
For community users, feed post editing is available only if the community was created using either Salesforce Tabs + Visualforce or the Customer Service template.
Given you meet the above, user's need the ...