I have the following use case that I am not sure whether can be achieved using any of Alfresco's API.
My team is currently developing a training application. We want to include a search textbox and button in our application. When the user enters his search string in our text box and click on the Search button, we want to send this search request to Alfresco application and display the search results in the Alfresco web ui. Is this possible to do and if so, how? Thanks.
Sure it is possible - that is actually how advanced search in Alfresco Share works. The form input of the advanced search is turned into a JSON string and inserted as an argument to the URL for the search result page, which then processes that input and forwards it to the actual search operation. So you can build something similar where your search UI constructs the URL to the Share search result page...