Most likely it's be ADSL2+
There's a good chance that both old and new logins will work concurrently for a bit, why not just plug the HH4 in and see if the light goes blue ?
As for the reboot thing .... my 4 has been rock solid for ever, mind you, I'm on FTTC.
I'm on FTTC and it makes no difference
Can you post your event log (Category: boot)
Recorded events
Time and date Message
14:40:51, 06 Sep. ( 21.320000) Booting firmware 4.7.5.1.83.8.130.1.17 (Type A)
17:37:21, 30 Aug. ( 20.140000) Booting firmware 4.7.5.1.83.8.130.1.17 (Type A)
17:21:10, 16 Aug. ( 20.120000) Booting firmware 4.7.5.1.83.8.130.1.17 (Type A)
17:05:04, 02 Aug. ( 19.880000) Booting firmware 4.7.5.1.83.8.130.1.17 (Type A)
11:47:56, 18 Jul. ( 20.030000) Booting firmware 4.7.5.1.83.8.130.1.17 (Type A)
11:31:54, 04 Jul. ( 19.850000) Booting firmware 4.7.5.1.83.8.130.1.17 (Type A)
11:12:52, 20 Jun. ( 19.830000) Booting firmware 4.7.5.1.83.8.130.1.17 (Type A)
10:55:14, 06 Jun. ( 13.890000) Booting firmware 4.7.5.1.83.8.130.1.17 (Type A)
00:00:14, 01 Jan. ( 14.320000) Booting firmware 4.7.5.1.83.8.130.1.17 (Type A)
00:00:13, 01 Jan. ( 13.870000) Booting firmware 4.7.5.1.83.8.130.1.17 (Type A)
00:00:14, 01 Jan. ( 14.320000) Booting firmware 4.7.5.1.83.8.130.1.17 (Type A)
00:00:13, 01 Jan. ( 13.680000) Booting firmware 4.7.5.1.83.8.130.1.17 (Type A)
(6th Sep was a manual reboot from me as I was troubleshooting torrent problem)