Before:
Click image for larger version. 

Name:	1.PNG 
Views:	291 
Size:	13.7 KB 
ID:	7959
After:
Click image for larger version. 

Name:	2.PNG 
Views:	305 
Size:	16.8 KB 
ID:	7960

Remove Search Icon from Windows 10 Taskbar:
1. Type regedit in RUN or Start search box and press Enter. It'll open Registry Editor.
2. Now go to following key:

HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion
3. Create a new key under CurrentVersion key and set its name as Search
So the final key path would be:

HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Search
4. Now select Search key and in right-side pane create a new DWORD EnableProactive and set its value to 0
Click image for larger version. 

Name:	3.PNG 
Views:	69 
Size:	26.6 KB 
ID:	7961
5. Restart, log off or restart Explorer to take effect.
PS: If you want to restore the icon in future, either set the DWORD values to 1 or delete the DWORD.
NOTE: This will not remove the Bing 'Everywhere' Search Engine from your system



Remove Task View Icon from Windows 10 Taskbar:
1. Type regedit in RUN or Start search box and press Enter. It'll open Registry Editor.
2. Now go to following key:

HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer
3. Create a new key under Explorer key and set its name as MultiTaskingView
4. Create another new key under MultiTaskingView key and set its name as AllUpView
So the final key path would be:

HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\MultitaskingView\AllUpView
5. Now select AllUpView key and in right-side pane create a new DWORD Enabled and set its value to 0
Click image for larger version. 

Name:	4.PNG 
Views:	69 
Size:	28.9 KB 
ID:	7962
6. Restart, log off or restart Explorer to take effect.
PS: If you want to restore the icon in future, either set the DWORD values to 1 or delete the DWORD.
NOTE: You can still create 'Virtual Desktops' by using WIN+CTRL+D; close an existing desktop using WIN+CTRL+F4; and switch between desktops using WIN+CTRL+Left or Right Arrow keys.