To Answer your question NO is probably the answer you will find, not at anywhere near the number your thinking of.
if the memory screen shot is correct you only have 100MB of ram (i suspect its cut off) EDIT it shows 1GB ram
The screenshot looks awfully like its from the cpanel interface which is more than definitely not tailored and optimized for your possible use case so performance would be far less than optimal
as the comments suggest, how many requests you can receive and process depends totally on what your doing with them. but with hardware that spec i doubt its even possible for the box to even receive that number of requests in the time frame you want
companies that do API processing on that level tend to have multiple (large) servers dedicated to the task of processing that data and be load balanced between them for HA also
nothing beats doing proper research and testing, why not test a smaller amount of queries and monitor performance, test and different levels and graph average performance metrics and you should be able to work out what you actually need or what the box is actually capable of