It’s up to you - WD reds have a better MTBF (mean time between failure - i.e., how long they’re expected to run for before, on average, you get an error or a failure). Lots of people swear by WD reds and plenty of people say that Seagates are fine. A lot of it depends on how much you care about a failure. For me, I run RAID, so I can lose a drive without losing everything. But if I lose 2 drives (e.g., a 2nd drive fails while I’m replacing the first), I then lose data, so have to start restoring from backups etc, which is a royal PITA. So I’m happy to spend a little more on WD Reds so that hopefully there’s less chance of multiple failures at the same time. If restoring from backups is quick and easy, or you have stuff you don’t care about losing, then potentially cheaper drives make sense as even if you have multiple failures, you’re back up and running quickly. Bear in mind that you might see better performance from the WDs too, although I suspect most people won’t ever notice a difference. For what it’s worth, I’ve had a 4-bay NAS running for several years, and only ever had a one disk fail. I swapped it with a new one and the array rebuilt itself, and WD sent me a free replacement.
One other tip - if you do order multiple drives, don’t order them all at once. Either spread the order over a few days, or better still order from a couple of different distributors. That way, you’ll get drives from different batches, which means that statistically they’re less likely to all fail at the same time.
Yes, you can do this. However, to get 20TB from 2x10TB drives leaves you with zero redundancy. If you’re running RAID0, and one of the drives fails, you could lose everything. Usually people would run 3x10TB and have one giving redundancy for the scenario above - which would give you 20TB and the ability to have a drive fail without any drama. Again, it depends on how painful it would be for you to restore your data. If you don’t mind a complete restore from backup then RAID0 is fine. If that’s going to be inconvenient, factor in some redundancy. I have 4x6TB in my NAS, which gives me around 16TB and a hot spare.
Have a read about disk sizes too - and get the largest disks you can. For example, if you were to do 2x10TB but in RAID (giving you 10TB + redundancy) then you could add another 10TB disk later and double your space. But if you did 2x6TB and then added a 10TB disk later, you may only be able to use 6TB of that disk. RAID is complex. 
I sidestepped the whole issue by buying my 916+ with 8GB pre-populated.
Connect them both to your network at the same time, then just copy from the old server’s network share. It’ll take a while, but you won’t have to babysit it. I’d recommend rclone or rsync to do the copy, depending on how the shares are set up.
You can connect in using a command line terminal session (Synology is basically linux). There’s also a bunch of web-based apps for managing the Synology box, including a download client (DownloadStation) and a File manager. There are also Android and iOS apps for these functions too. So for example, I can kick off a download via the Android app DS Get, and when it’s complete move it to another folder via the DS File app. From a user perspective, the Synology has a very strong ecosystem offering.
