>Are these devices connected to VR1600V by wirelessly? Please try to change different wireless name and password on your router and see what happens?

>What are their IP addresses?

The set-top box is currently 192.168.1.106 and the NAS is 192.168.1.107

>Try to ping the gateway of VR1600v(192.168.1.1) and ping 8.8.8.8 and show us the pictures of ping results.

Here are the ping results from the NAS

> Meanwhile, cause they are NAS and set-top box, it is suggested to contact their tech support to verify whether there is any special settings need to be done, like port forwarding or so.

To my knowledge, the set-top box does not require any special settings - the technician who performed the installation suggested that I contact my ISP. The NAS was able to work properly without port forwarding on my previous router (Archer VR600). Unfortunately I no longer have my previous router, so I cannot compare the configurations directly, but to the best of my knowledge there is no difference in how my current router is configured.

>It is suggested to change the DNS server to 8.8.8.8/8.8.4.4. Once you go to advanced-internet page, you can see DHCP server/LAN settings, then you can see the option to change DNS server.

I have already attempted this, and it did not work. I've tried again, and the NAS still cannot access the internet.

>Can other device access the NAS or the set-top box in the same network? 

My PC (which I am writing this from) is able to access the NAS over the network. I used SSH to get the NAS to try pinging 8.8.8.8 as you suggested earlier.

>Meanwhile, does your NAS support routing tracking function

Here are the results of an attempted traceroute on 8.8.8.8 from my NAS

>Besides, please tell me the current hardware and firmware version.

Of the Router? As I said, it's an Archer VR1600V

Hardware version: v1 00000000

Firmware version: 0.1.0 0.9.1 v5006.0 Build 180828 Rel.56416n

This describes a similar problem that I had with connecting an Android Sony TV to the internet via a VR1600v and a work around for the problem.

My setup:

NBN Technology:    NBN Hybrid Fibre Coaxial (HFC) 
ISP:                        TPG
Plan:                       NBN Cable 50
NBN modem:         ARRIS Model CM8200B
tp-link modem/router:
Hardware Version:     Archer VR1600v v2 00000000
Firmware Version:     010091 v5006 0 Build 190228 Rel 72265n

Computer:                Dell Optiplex 9010
OS:                          Windows 10 Pro Version 1809 Build 17763.529

Default Gateway:     192.168.1.1
DHCP Server:          192.168.1.1
DNS Servers:           192.168.1.1
                                 203.12.160.35
DOS Protection:        Enabled
Access Control:        On
Access Mode:           Whitelist
Devices in Whitelist:    List of connected MAC addresses
    PC
    iPhone
    iPad
    android smart TV 
        Sony  Bravia KD-55X9000F
        Kernel version 3.10.79 root@BuildHost597 #1
        BuildBRAVIA_ATV3_4K_PA-user 7.0 NRD91N.S139
        1.6.0.56.29.1.00 release-keys

I had trouble with getting an internet connection from the TV.
There was no problem with the PC, iPhone and iPad.
The TV would connect to the VR1600v via 2.4 wireless, 5G wireless and LAN cable, but would not get an internet connection. The wireless connections were setup by manually selecting the networks to join.
The TV would report that a wireless connection was made but that it could not connect to the internet. The was confirmed by navigating to the Network Status page from the TV settings page and performing a connection test. This showed:
    Wireless device on TV:    found
    Local access:        {Ipv4:OK][IPv6:Failed]
    Internet access:    [IPv4:Failed][IPv6:Failed]
The Network status page showed Good for 2.4 and Fair for 5G.

I had a similar problem setting up the TV with the ADSL2+ Huawei HG532d WiFi but was able to resolve the problem by setting the DNS server IP addresses as listed above.
With the VR1600v, setting the DNS IP addresses did not help.
My thought  was that something in the VR1600v was preventing the TV device from getting the internet connection. Also that it must be a problem with the TVs implementation of the protocol since that other devices connected successfully.
One thing to try was to remove the Access Control Whitelist specifications.

To do this I used the web interface for the VR1600v to reset to the factory defaults, which also rebooted the VR1600v. I then re-entered the device settings that I wanted, but omitting the whitelist - just leaving a blank Blacklist.
Retesting the TV WiFi connection gave an internet connection for IPv4 straight away.
So it seems that the problem is caused by the interaction of the VR1600v Whitelist system and the Sony Android TV protocol handing.