fsck not working and can´t open .dmg after 10.15.2 update

If the system is still bootable, then try the following:

A Troubleshooting Procedure that may Fix Problems with macOS El Capitan or Later

You should try each, one at a time, then test to see if the problem is fixed before going on to the next.

    Be sure to backup your files before proceeding if possible.

1. Shutdown the computer, wait 30 seconds, restart the computer.
2. Disconnect all third-party peripherals.
3. Resetting your Mac's PRAM and NVRAM
4. Reset the System Management Controller (SMC)
5. Reset your Startup Disk and Sound preferences, if needed, after resetting the PRAM.
6. Test in safe mode to see if the problem persists, then restart normally.  Use safe mode to isolate issues with your Mac and Playing Safe - what does Safe mode do?
7. Repair the disk by booting from the Recovery HD. Immediately after the chime hold down the Command and R keys until the Utility Menu appears. Choose Disk Utility and click on the Continue button. Select the indented (usually, Macintosh HD) volume entry from the side list.  Click on the First Aid button in the toolbar. Wait for the Done button to appear. Quit Disk Utility and return to the Utility Menu. Restart the computer from the Apple Menu.
8. Repair permissions on the Home folder: Resolve issues caused by changing the permissions of items in your home folder.
9. Create a New User Account Open Users & Groups preferences. Click on the lock icon and enter your Admin password when prompted. On the left under Current User click on the Add [+] button under Login Options. Setup a new Admin user account. Upon completion log out of your current account then log into the new account. If your problems cease, then consider switching to the new account and transferring your files to it - Transferring files from one User Account to another.
10. Re-download the Catalina updater and reinstall it. macOS Catalina 10.15.2 Update.
11. Reinstall OS X by booting from the Recovery HD using the Command and R keys. When the Utility Menu appears select Install OS X then click on the Continue button.
12. Erase and Install OS X Restart the computer. Immediately after the chime hold down the Command and R keys until the Apple logo appears. When the Utility Menu appears:

     1. Select Disk Utility from the Utility Menu and click on the Continue button.

     2. When Disk Utility loads select the drive (out-dented entry) from the Device list.

     3. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.

     4. Set the Format type to APFS (for SSDs only) or Mac OS Extended (Journaled.)

     5. Click on the Apply button, then wait for the Done button to activate and click on it.

     6. Quit Disk Utility and return to the Utility Menu.

     7. Select Install OS X and click on the Continue button.

I think the question would be how are you using the command line and from where?

You do not say what exact Mac you are using?

Apple details this here, and recommends that, if your Mac has a T2, you:

1. Start up in Recovery Mode, using Command-R.
2. Open Disk Utility, select your normal boot volume, and mount it using the Mount command in the File menu, if necessary.
3. Close Disk Utility and switch to Terminal.
4. Run your desired commands in Terminal, using tools on your mounted boot volume as required.

The updates don't break things, rather it's the underlying system installation that is already broken such that the update/upgrade makes things even worse. Updates cannot "fix" already broken systems.

Repairing permissions on your Home folder is not out of date even for Catalina. User mistakes or third-party software may alter permissions in the Home folder causing functional problems. These problems can often be repaired by resetting permissions in the Home folder to their default state. This has nothing to do with fsck.

Fsck is merely a filesystem check and repair program. It is what Disk Utility uses. All macOS tools are mostly GUI wrappers around a Unix command, like fsck. You ran it in verbose mode (single-user mode) but did not report results. You simply said there was an fsck problem. Therefore, there is no way to determine what happened or why.

If you got all the way to the point of doing an Erase and Install, then your system was so badly hosed that not even a simple re-install could fix things. You may consider doing these updates/upgrades with some sort of planned order. Here is my suggestion:

1. Use Disk Utility to run First Aid on the disk that is being updated.
2. Create a bootable backup of the startup disk on an external disk.
3. Test the backup to be sure it properly boots the computer.
4. If you have already downloaded the installer, then transfer it to the bootable backup. Otherwise, directly download the installer to the bootable backup.
5. Reboot the computer from the bootable backup but boot into Safe Mode.
6. Open the macOS installer app.
7. Change the target disk to the computer's main boot disk. This will not work with updaters. Updaters will have to run from the target disk. However, if you install the update on the backup disk, then you can determine if the update was successful. If it is, then clone the backup to the computer's main boot disk or install the update directly after booting from the main boot disk. If there is a problem, the problem will not affect the computer's main disk, and you lose no down-time.

Here is an alternative to the above:

Installing An Upgrade From Safe Mode

1. Disconnect all peripherals connected.
2. Reset your Mac's PRAM and NVRAM.
3. Restart the computer and at the chime press and hold down the Command and R keys until the Utility Menu appears.
4. Select Disk Utility and press the Continue button.
5. Then select the indented (usually, Macintosh HD) volume entry from the side list. 
6. Click on the First Aid button in the toolbar and wait for the Done button to activate. Click on it, then quit Disk Utility.
7. Select Restart from the Apple menu. Press and hold down Command-S to start in safe mode. This is slower than a normal startup. Don't panic.
8. Now, try installing the update/upgrade, and see if you have normal results.