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You can use many softwares for mining the web data like there are different ETL tools like pentaho,SQL Server Integration services or there are some other tools also like R or python all you have to write an API to extract data from the web.
Yes, there are many web mining algorithms. The difference among them is their application. Weka is a good application from the university of Waikato in New Zealand, sums up work from a lot of algorithms in one application. Depending on the type of data for machine learning different mining algorithms are used.