Would router upgrade help with slow transfer speeds between NAS540 and PC

Would something like this be enough?
ZYXEL NBG6716 AC1750
https://www.amazon.com/ZyXEL-Simultaneous-Dual-Band-Wireless-NBG6716/dp/B00FRX2U1W
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Mijzelf Member Posts: 1,498
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What could be the bottleneck?For instance the nature of the data you are copying. If you are copying a lot of small files, the disks can be the bottleneck. While a modern rotating disk can easily write at 150MB/sec, the random access time (the time to position the heads above a certain sector) is something like 10msec. Writing a file hits at least 2 times that random access time. Once to write the directory entry, once to write the file itself. When some filesystem structures have to be accessed to find free space for that file, that could easily get 3 or 4 times. So you can't write more than 25~50 files a second. If each file is 1 byte, you'll get a throughput of 50B/sec. (BTW, that's the reason an SSD feels so fast. It's not the throughput, but the random access time. For an SSD that is measured in nanoseconds.)
If I go for a new router I would have faster connection speed between the NAS and the laptop even wirelessly, is that correct?Yes. Assuming the laptop isn't limited on 300Mbit wifi.
If I understand correctly, the connection between an external HDD and the NAS, even when it is connected to the USB port on the NAS is handled by the laptopDepends. If you are using the 'copy' button, it's handled completely by the NAS. If you use the filebrowser in the webinterface, it's also handled by the NAS. Only if you copy from a share on the external disk to a share on the internal disk, it's handled by the laptop.
If so, what would be an entrance level Gigabit Router that you would recommend me?Sorry, I have no opinion on that. Search for a router on base of specs, and than read reviews. And keep in mind, it doesn't pay to have router that performs far better than your clients. Also not for future use. When you buy a 'better' laptop next year, the top spec router from today will be entry level, and cost accordingly.
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What should I look for in a switch? Is there anything I need to know?
Plus, I would now get 80+ mbs when I get the switch, right?
Maybe. The NAS can do 80+MB/sec (please use the right case, mb is something different!) under certain circumstances. But your speed is now not near the 11MB/sec which fast ethernet could do. So possibly the network is not the bottleneck.
If so, what would be an entrance level Gigabit Router that you would recommend me?
Though I'm already sold on the Gigabit Switch idea. If I understand correctly, the connection between an external HDD and the NAS, even when it is connected to the USB port on the NAS is handled by the laptop, so with the use of a Gigabit Switch the laptop and the NAS will communicate inside the switch, it will also speed up the transfer speed between external HDD connected to the usb3 port of the NAS and the NAS. Is that correct?