Will the presets be saved on another computer?

no, you will need to manually save those things for each adobe program from your old computer and move them to your new computer.  

eg, here's how to find the preference files

acrobat: https://forums.adobe.com/thread/1595848?start=0&tstart=0
adobe media encoder: https://forums.adobe.com/thread/1713540
after effects: http://helpx.adobe.com/after-effects/using/preferences.html
audition: https://forums.adobe.com/thread/1079494
bridge: https://helpx.adobe.com/bridge/kb/troubleshoot-errors-freezes-bridge-windows.html
captivate: https://forums.adobe.com/thread/975032
dreamweaver: https://helpx.adobe.com/dreamweaver/kb/restore-preferences-dreamweaver-cs6-cc.html
flash: https://helpx.adobe.com/animate/using/set-preferences.html
fireworks: https://helpx.adobe.com/fireworks/kb/restore-preferences-fireworks-cs5.html
illustrator: http://helpx.adobe.com/illustrator/using/setting-preferences.html
incopy: https://forums.adobe.com/thread/526990
indesign: https://forums.adobe.com/thread/526990
lightroom: https://helpx.adobe.com/lightroom/help/setting-preferences-lightroom.html
muse: https://forums.adobe.com/thread/1127564 (message 7)
photoshop: https://helpx.adobe.com/photoshop/using/preferences.html
photoshop elements: https://helpx.adobe.com/photoshop-elements/kb/preference-file-locations-photoshop-elements.html, http://www.photokaboom.com/photography/learn/Photoshop_Elements/troubleshooting/1_delete_preferences_file.htm
prelude: https://helpx.adobe.com/prelude/using/prelude-set-preferences.html
premiere elements: https://helpx.adobe.com/photoshop-elements/kb/preference-file-locations-photoshop-elements.html
premiere pro: http://www.mediacollege.com/adobe/premiere/pro/troubleshooter/trash-preferences.html