How can I can convert ticker symbols ... to an International Securities Identification Number (ISIN) ... ?
As @Indian Rediff said in this answer, it is not possible in general to convert or map stock ticker symbols to ISIN's or vice versa using a number of rules or a mathematical function.
However, you can find out the ISIN for a stock by searching for its ticker symbol or name on this web page on Stock Market MBA. After you make such a search, locate the row that appears to show the characteristics of the security you are looking for and click on the "Analyze" option under the "Actions" column. This will open up a new page including an "Intro" tab whose contents would include the ISIN of the security along with its many other characteristics.
... given an ISIN and a market identification code (MIC) how can I determine the ticker symbol?
You can find out the ticker symbols and exchanges associated with a stock by looking up the security's ISIN on this web page on Stock Market MBA again.
These features on the mentioned web site are not only free (at least for now) but also has extensive international coverage based on the data from OpenFIGI which is also mentioned in this answer by @John Wood.
Update (12 October 2022)
While one still can look up an ISIN on Stock Market MBA, it appears it is no longer possible to look up the ticker symbol of a stock and get the ISIN on the same site, only the SEDOL.