I've used Thecus NAS's for many years, recommended them to co-workers and friends seeking the same kinds of solutions.  Back when I was looking to go way beyond local USB-connected hard drives for my home network, I did my own research into what existed for NAS solutions at the time (2010-2011).  I had looked into QNAP, WD World, Synology, FreeNAS, etc...

FWIW, I bought my first NAS from Thecus, the N7700SAS with seven 2TB drives in 2011.  I used RAID5 with approximately 11T of storage.  The N7700SAS NAS is still operational, with about 98% uptime (in the last year it has begun to shut itself off on its own periodically).  Other than that, it has been ROCK solid.  Since then I've bought the N5550 (five drive bays) in 2017 and have five 14TB drives in it, under RAID5.  Again, it is rock solid and I've been running it at 99.99+ uptime.  It meets all your bullets (which I've numbered), with the following caveats:

-  Bullet 3: that is up to how you allow access to the NAS via your firewall/network topology.

-  Bullet 6: that too is up to how you allow access to the NAS via your firewall/network topology.

Thecus does a really good job of testing and validating a variety of memory and hard drive configurations; and they also provide insights into drives they've tested/recommend, and those they do NOT recommend (and usually why); same for memory chips.  They keep their compatibility guides up to date.  For the N5810, you can, for example use five Western Digital Red Wolf Pro drives with a capacity of 18TB each.  I use the raid calculator site (raid-calculator.com) to test out various RAID vs size comparisons.

You can buy the Thecus n5810 tower 'shell' and separately purchase/supply the drives you want.  Currently the n5810 and n5810PRO are viable options.  The distinction is that the PRO version has a built-on UPS.  You'll have to evaluate for yourself the value of that configuration.  Additionally, they have other SOHO options (the n4350 and n2350; in four and two drive form-factors, respectively).

This is a spinning-disk solution, by the way.  Though Thecus has begun to build/test NAS solutions with SSD's, I've not yet seen a viable high-capacity SSD-based NAS from them---though still looking and hopeful.

Were I going to purchase another NAS today, I'd go with the N5810.

It is kinda difficult through Thecus's web site to discover where you can go to buy their products.

I found 'networkstorageworks.com' to be one that is reasonable in price. 

I'm not affiliated with Thecus nor networkstorageworks, simply a long-time happy Thecus customer.

-Joe