Should I be concerned about....

[#1]

Should I be concerned about CRC and HEC errors? My IP profile has dropped to 3500k and won't seem to come back up after two weeks now.

Link Information

Uptime: 0 days, 20:16:15
DSL Type: G.992.1 annex A
Bandwidth (Up/Down) [kbps/kbps]: 448 / 6,912
Data Transferred (Sent/Received) [kB/kB]: 0.00 / 0.00
Output Power (Up/Down) [dBm]: 11.5 / 19.5
Line Attenuation (Up/Down) [dB]: 18.0 / 29.0
SN Margin (Up/Down) [dB]: 24.0 / 15.0
Vendor ID (Local/Remote): TMMB / TSTC
Loss of Framing (Local/Remote): 0 / 0
Loss of Signal (Local/Remote): 0 / 0
Loss of Power (Local/Remote): 0 / 0
Loss of Link (Remote): 0
Error Seconds (Local/Remote): 9 / 0
FEC Errors (Up/Down): 0 / 0
CRC Errors (Up/Down): 0 / 803
HEC Errors (Up/Down): 0 / 652

[#2]

No is the quick answer - they are low considering you have been connected for over 20 hours
Regarding your IP pofile - assuming you are checking using the BT speedtester then you need to raise a ticket asking for a check of the radius logs as it should have risen.
Alternatively if it is the speed reported from the Plusnet site then you need to check the IP profile using the BT speed tester then raise a ticket asking for the Plusnet profile to be raised to match the BT one.

[#3]

Looking at my SNR margins, I should be able to easily sync at full 8192k shouldn't I?

[#4]

The fact that your profile dropped to 3,500 indicates that there was a low sync event - which is surprising given the 15dB noise margin
The noise margin would, I expect, have been raised from 6dB to 15dB because of instability and errors on the line.
The first thing you should do is try to see it your internal wiring is responsible.
If you connect the router to the test socket without any phones connected what are the reported stats.
The other things I would ask is why did the router resync yesterday evening and how do you know your router has been connected at 6,912 for 2 weeks

[#5]

2 weeks ago, I had a fault which involved awful crackling on the line, followed by loss of dialtone.  This happened on and off for a week.  The dialtone and crackling would go away and come back randomly. (Anyone with similar experience?)
I think this problem is fixed, although with things not improving I'm beginning to suspect not.  I know the router has been syncing at 6k because I've been monitoring it daily.  The restart 20 hours ago was initiated by me to see if it would re-train at better rates.

[#6]

Crackling on the line usually indicates a Line fault probably caused by water ingress to a cable or junction box. This could be underground or on an overhead line where the outer sheath of the cable gets scuffed and wicks water up the cable to the junction box on a pole or a cabinet. It has been so wet here that we have water fountains coming out of the cable duct covers on the pavement!
You should report the fault to your Telephone provider and get them to acknowledge that they can hear the crackling. Also, be sure to unscrew the NTE5 Faceplate and check that the noise is present with a single Handset plugged into the Master Socket.
I will relate a tale of my daughter's phone whic went dead last week. I called the fault in to Primus Planet Talk at 11:00 hrs and went down about an hour later to check the Master socket. I had just taken off the faceplate to find that I got a dialtone on the Master Socket when the Doorbell rang and there was the Openreach man!!!
Luckily, he found two faults... one with the NTE5  which had disintegrated such that the Master socket was floating free .... and the other, a faulty BT MF50 Microfilter on the USER SIDE! The very nice man was magnanimous enough to attribute the fault to the NTE5 and  replaced it with a brand new Openreach model.
It didn't cost me the £160 callout charge but i did give him my Leatherman Micra Multitool which I has been using and was much admired by him. So, the moral is that when Tea and Buscuits don't work, try a Boy's toy.