You have adware/malware installed. Use Malwarebytes Anti-Malware for Mac. It may be necessary to run more than one scan. After scanning a couple of times, restart the computer and test. If necessary, follow the manual instructions. Do not download any other programs that are listed in the articles. Malwarebytes uninstall
Search.anysearch.net uninstall
For the App Store problem, are you running any anti - virus programs? Using a VPN?
Try setting up another admin user account in System Preferences/Users & Groups to see if the same problem continues. Please post back on whether or not this worked. Also try the Safe Mode. Please post back on whether or not this worked.
Isolating an issue by using another user account
Safe Mode - About
If it works in the Safe Mode, try running this program when booted normally and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor. Please use copy and paste as screen shots can be hard to read. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown. If the log won’t post, try posting it in Pastebin and provide a link in a reply. After pasting the report in a PasteBin page, go to the top of the page, and copy the address in the URL bar. Paste that in a new reply. Pastebin
Etrecheck – System Information
Web site version if required. https://etrecheck.com