If I reinstall the game will the installed sims3packs show up or no, because there is no files in the Download section in the sims 3 launcher?

Edit: I tried to open a file in the DCbackup folder and the windows said that it will open the file in utorrent, but I automatically clicked yes, and now all the files in that folder show up with utorrent icons, but the file name still says they"re .package files. Is this a problem or not?

If there's a reason to reinstall the game? - it's a nuclear option, really not needed until the game data is damaged or you change the machine. If it's not the case - just renaming the SIms3 user folder (within "My Documents" tree) shall force the game to create a new, clean one and the program behaviour will return to "like fresh installed".

Custom Content installed by Launcher is placed in DCCache and in the Installed Worlds (literally: the 'world' files) folders, families are landing in the "Library" and downloades sims (*.sim file)within "SavedSims".
Copying them from old Sims 3 user folder to the new one should completely restore the content. The same case is the "Mod" subtree (package type CC) within the Sims3 directory.

In the future it's possible that I'll get a new laptop, that's why I asked.

No, it's not really a problem that your .package files are associated with Utorrent as long as you don't accidentally double-click them and activate it when you don't want to. As long as they are .package files the game can read them. You can also get Packer from NRAAS or S3PE from that link and let them get associated with one of those programs if you prefer.

If you deleted your Sims3packs, they are gone. They are EA's version of an archive, like zip or rar. The game unpacks them in order to install them. If you haven't emptied your recycle bin they might be there. Otherwise, yes. You need to redownload them if you want them back. But they don't need to stay in Downloads. Once you've installed them you can move them to a separate folder somewhere else (even onto a flash drive) and they will be fine.

You might prefer to be sure that you backup your Documents Sims 3 folder and copy everything over to the new game if you ever reinstall.

Edit: I got ninja'ed

except for DeviceConfig.log and Option.ini, these two depends on computer's spec, don't copy and paste them, use the ones that generated by TS3 in your new laptop once you run the game at least once.