Can I access HDFS files from Custom web application
If your application is written in Java, this is easily possible using the DFS Client libraries which can read and write files in HDFS in a very similar way to a standard filesystem. Basically can open an input or output stream and read whatever data you want.
If you are planning to use python to build the web application, then you could look at webHDFS, which provides a HTTP based API to put and get files from HDFS.