Then how about other coins?
What about reading the other answers?
Since you are able to build a web application, you shouldn't have any problems understanding the links mentioned by HCP:
The article regarding what happened from v0.15 with regards to fee estimation is here: https://bitcointechtalk.com/whats-new-in-bitcoin-core-v0-15-part-2-41b6d0493136
You will be able to estimate the fee yourself after reading those articles. The implementation itself is trivial. Examples can be found on the internet.
By implementing it yourself you are independent from API service provider (which can have wrong information / downtimes and do not exist for all cryptos).