[Galaxy Note GT-N7000 Android Development] aidjek:
Oh, okay. I will take an attention at this in the next time, but I guess I know there were my faults in the previous attempt to install recovery.

Very productive advice, the solution for my case is presented below:

pre-solution several facts:

my flashing road map in last night were:

first attempt:

Flash PhilZ-cwm6-XXLT6-XSA-5.06.1.tar.md5 via Odin -> go in the Recovery Mode -> Clean to install new ROM (it's showing me that /data, /system, /cache and several partitions were formatted) -> Flash Beta5.zip -> Flash last kernel Nightowl-cm13-20161012-n7000-kernel_only.zip (for some reason) -> NO reboot to recovery -> Flash last GAPPS -> Format Cache one more time -> Rooting device from Recovery - and it was wrong way, after 1,5 hour of waiting, I rebooted the device and received broken recovery and firmware

second attempt:

Flash PhilZ-cwm6-XXLT6-XSA-5.06.1.tar.md5 via Odin -> go in the Recovery Mode -> Clean to install new ROM (it's showing me that /data, /system, /cache and several partitions were formatted) -> Flash Beta5.zip -> Flash last GAPPS -> Format Cache one more time -> Rooting device from Recovery - and system started but root has not working, as it was several days ago (kernel has not flashed in this attempt).

After ROM Toolbox Pro I have in my Apps List Busybox and RootChecker applications. And I didn't pay attention on their automatically installation after LineAgeOS configuration scenario.

Solution:

install adb from https://developer.android.com/studio/releases/platform-tools.html#download

configure on your device in Settings -> Developer Options -> Root Access set to Apps and ADB | Android Debugging (Enable the Android Debug Bridge interface) set to Enable | Local Terminal set to Enable

start adb with shell in one PowerShell window

GT_N7000_firmware\platform-tools> .\adb.exe shell

and adb with logcat in the another PowerShell window

GT_N7000_firmware\platform-tools> .\adb.exe logcat

you must observe that adb shell has gone in the root mode automatically

PS D:\vmware_share\Dropbox\GT_N7000_firmware\platform-tools> .\adb.exe shell
←7←[r←[999;999H←[6n←8n7000:/ #
n7000:/ #
n7000:/ # whoami
root
n7000:/ # su
n7000:/ # whoami
root

after su command in logcat you will see:

03-29 12:01:50.492 13722 13722 D su : su invoked.
03-29 12:01:50.493 13722 13722 D su : starting daemon client 0 0
03-29 12:01:50.522 13725 13725 D su : remote pid: 13722
03-29 12:01:50.530 13725 13725 D su : remote pts_slave: /dev/pts/3
03-29 12:01:50.533 13725 13725 D su : waiting for child exit
03-29 12:01:50.535 13727 13727 D su : daemon: stdin using PTY
03-29 12:01:50.535 13727 13727 D su : daemon: stdout using PTY
03-29 12:01:50.535 13727 13727 D su : daemon: stderr using PTY
03-29 12:01:50.539 13728 13728 D su : su invoked.
03-29 12:01:50.542 13728 13728 E su : SU from: root
03-29 12:01:50.542 13728 13728 D su : Allowing root/system/radio.
03-29 12:01:50.542 13728 13728 D su : 0 /system/bin/sh executing 0 /system/bin/sh using binary /system/bin/sh : sh
03-29 12:01:50.544 13728 13728 D su : Waiting for pid 13729.

if you try to run any application which require root (Titanium Backup, LogCat, RootChecker) from device you will see next error in logcat from adb:

03-29 12:02:26.966 5445 5445 D Terminal: setColors(0xffffffff, 0xff000000)
03-29 12:02:27.102 5445 5445 D Terminal: resize(30, 50, 100)
03-29 12:02:27.112 5445 5445 D Terminal: Bound to service with 1 active terminals
03-29 12:02:27.802 5445 5445 D Terminal: resize(14, 50, 100)
03-29 12:02:38.910 14002 14002 E su : must not be a setuid binary
03-29 12:03:01.568 14028 14028 E su : must not be a setuid binary

03-29 12:03:17.849 14041 14067 I com.keramidas.TitaniumBackup.MainActivity: Applying SELinux security context to: "/data
/user/0/com.keramidas.TitaniumBackup/files/busybox"
03-29 12:03:17.892 14069 14069 E su : must not be a setuid binary
03-29 12:03:18.421 14078 14078 E su : must not be a setuid binary
03-29 12:03:18.442 14081 14081 E su : must not be a setuid binary

let's check su binary permissions from adb shell

n7000:/ # ls -la /system/bin/su
lrwxr-xr-x 1 root shell 10 2009-01-01 01:00 /system/bin/su -> ../xbin/su
n7000:/ # ls -la /system/xbin/su
-rwsr-sr-x 1 root shell 112580 2009-01-01 01:00 /system/xbin/su
n7000:/ # stat /system/bin/su
File: `/system/bin/su' -> `../xbin/su'
Size: 10 Blocks: 0 IO Blocks: 512 symbolic link
Device: b309h/45833d Inode: 413 Links: 1
Access: (755/lrwxr-xr-x) Uid: ( 0/ root) Gid: ( 2000/ shell)
Access: 2009-01-01 01:00:00.000000000
Modify: 2009-01-01 01:00:00.000000000
Change: 2009-01-01 01:00:00.000000000
n7000:/ # stat /system/xbin/su
File: `/system/xbin/su'
Size: 112580 Blocks: 224 IO Blocks: 512 regular file
Device: b309h/45833d Inode: 1987 Links: 1
Access: (6755/-rwsr-sr-x) Uid: ( 0/ root) Gid: ( 2000/ shell)
Access: 2009-01-01 01:00:00.000000000
Modify: 2009-01-01 01:00:00.000000000
Change: 2017-03-29 00:30:08.242856218

let's try to change permissions, but read-only filesystem occurs

n7000:/ # chmod 0755 /system/xbin/su
chmod: chmod '/system/xbin/su' to 100755: Read-only file system

going to mount for checking partitions and remount it in rw mode

1|n7000:/ # mount
rootfs on / type rootfs (ro,seclabel,relatime)
tmpfs on /dev type tmpfs (rw,seclabel,nosuid,relatime,mode=755)
devpts on /dev/pts type devpts (rw,seclabel,relatime,mode=600)
proc on /proc type proc (rw,relatime)
sysfs on /sys type sysfs (rw,seclabel,relatime)
selinuxfs on /sys/fs/selinux type selinuxfs (rw,relatime)
none on /acct type cgroup (rw,relatime,cpuacct)
tmpfs on /mnt type tmpfs (rw,seclabel,relatime,mode=755,gid=1000)
none on /dev/memcg type cgroup (rw,relatime,memory)
none on /dev/cpuctl type cgroup (rw,relatime,cpu)
/dev/block/mmcblk0p9 on /system type ext4 (ro,seclabel,noatime,user_xattr,barrier=1,data=ordered)

n7000:/ # mount -o remount,rw /system
n7000:/ # mount
rootfs on / type rootfs (ro,seclabel,relatime)
tmpfs on /dev type tmpfs (rw,seclabel,nosuid,relatime,mode=755)
devpts on /dev/pts type devpts (rw,seclabel,relatime,mode=600)
proc on /proc type proc (rw,relatime)
sysfs on /sys type sysfs (rw,seclabel,relatime)
selinuxfs on /sys/fs/selinux type selinuxfs (rw,relatime)
none on /acct type cgroup (rw,relatime,cpuacct)
tmpfs on /mnt type tmpfs (rw,seclabel,relatime,mode=755,gid=1000)
none on /dev/memcg type cgroup (rw,relatime,memory)
none on /dev/cpuctl type cgroup (rw,relatime,cpu)
/dev/block/mmcblk0p9 on /system type ext4 (rw,seclabel,noatime,user_xattr,barrier=1,data=ordered)

and change binary permissions

n7000:/ # chmod 0755 /system/xbin/su

after this root has started to work correct and in any application.

My conclusions: I guess that busybox after install has remade symbol links and made su command under suid, which has made root broken.

I will try tonight to flash one more time my device with kernel and all stuff, but without busybox and rootchecker and will let you know if root has start to work after it.