Axiom air mini 32

You made a beat?  Using what synth or soft synth and played from the Axiom controller?
 
SONAR should keep the "beats" in tempo, as determined by, well the tempo SONAR is set at.  If you are using MIDI (played by the controller) it should be as tempo correct as you can play.  If you need to, you can go in and edit the notes - see the manual.
 
If you are using audio Acidized files (groove clips in SONAR speak) they will match the tempo set by SONAR.
 
Wave files won't - tho SONAR can turn them into groove clips.
 
Hope this helps, but until you clarify what you are doing to make your beats all advice is pissing in the dark.
 
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Sound Center is a soft synth.  So you were recording and playing back midi using a sample playback synth.
 
Beatport looks to be a sample shop (I've never used it).  I imagine what you have there are plain ole wav sounds.  You should be able to drag them directly onto the timeline from the browser.  However, they will be laid in as wav files, so if you change the tempo they will change pitch.  Groove clipping them requires that you double click on the wav file on the timeline and a page will pop up.  This allows you to trim and input the measures/beats/pitch in (or have SONAR figure it out).  A wav file will have straight corner edges - a groove clip will have blunted corners.  You should read the help files to get a handle on groove-clipping.
 
You don't need use ctrl to move sections of clips, just hold the mouse down to grab a section.  Do use the ctrl to add clips one at a time to the first highlighted one - and then let the ctrl go when you've highlighted all the clips you want to drag to a new location.
 
You are on the right path - it is a lot to learn.  The good thing about SONAR is it follows most of the windows conventions, so a lot of mouse motions are instinctive.