Not sure how you are trying to do the first query (this should be easily achieved with the normal advanced ticket search?) so more info would be helpful!
RE the number of search results there are two settings in Setup> General> Options, one which control the max number of returned results in a search & another controlling the max number of results displayed on a page which should help. If you do a search & then export out the results without ticking / checking any of the results it will export all the results; if you check the box at the top of the page of results it will only export that page of results.
If you are just after the figures it might be easiest to save your search as a query & then create a dashboard widget which uses that query.
I am trying to use the API for web helpdesk. I can do everything that i need in the GUI but we are wanting to use the API to product the data.
This is the query i'm using, the status type works fine just the tech group.
https://URL/helpdesk/WebObjects/Helpdesk.woa/ra/Tickets?limit=100&qualifier=((statustype.statusTypeName %3D 'Open') and (techGroupLevel.levelName like 'Group'))
With the API I am also trying to count all tickets including open, closed etc but the API has a limit of 100 (rather annoying) so was wondering if there is a different way.