1- When Should You File a Reconsideration Request?
A reconsideration request should be filed only after you have received a manual penalty notification in the Webmasters tools. You can file a reconsideration request from the Google Webmasters console. You must file a request only after you clean up your site or backlink profile which were going against Google Webmasters guidelines.
2- How to Check the Quality of Backlinks Pointing to Your Site?
You may check all the backlinks pointing to your website using the Google Webmaster tools. After logging in, move to Traffic -> Links to your site and you will see all the links that Google has discovered until now. You can get an idea of the sort of links being generated for your website.
3- How to Clean up Your Link Profile?
Cleaning up your link profile requires time and patience. A proper analysis of site backlinks is required followed by link removal by sending requests to webmasters and using the disavow tool as the last resort.
4- What is the Time Taken to Process Reconsideration Requests?
There is no specific time given by Google in this regard. However, most of the requests are processed in a few days