No. 1 is a bug, where the healing he got over the fight is not shown in the health bar. So, if you deal as much damage over the fight as his initial health was, his health bar will look empty for the rest of the fight. A lot of people mentioned that here in the forum allready, they should really start fixing the problem.

No. 2 self heals may come from gear. A regeneration set heals 15% of the max hp each turn, and a lot of people build UDK with this set. That's the reason why heal reduction is a good way to deal with UDK in arena. Blocking his passive heal, his healing from buffs and from his equip, and, at the same way, avoiding the bug from no. 1.

I see.  

regarding #2, why would regen set heal twice though?  isn't it a 4piece set?

Yes, regeneration is a 4 pieces set. There is another set that does some minor healing (3%), immortal. In that case, there should be different healing numbers, not 8k twice. But maybe your observation of the numbers was not correct and it was one big heal for 8k and a second, smaller healing.

Or there was another champion involved healing the UDK. Rector Drath, for example, heals allies under veil  by 10% of their health, and that in the allies turn. So an UDK with regenartion set and Rector as partner could get a 15% and a 10% heal at the start of his round. 

Everytime it was only UDK left. That's been my bottleneck at silver, the lone UDK after every fight.  I dunno maybe I did read wrong, but they are huge chunks of lifebar back.  Can't wait to finally have a strong enough answer for UDKs in silver.

Any champ with heal reduction debuff is a strong answer to single UDK.

i got lucky and got a coldheart yesterday.  gotta gear up though.  This is my first heal debuff option ever, hope it can work.

To your second point - UDK's passive causes him to heal when *you* heal as well. Perhaps that's where the bigger heals came from.

Too Awesome To Die (Passive)
Whenever an ally is attacked, has a 100% chance of completely blocking 1 hit, decreasing the damage to zero. This champion will receive that damage instead. The chance decrease to 50% if the attacker is a Boss. Does not work if the attack on the ally was an AoE attack. Whenever an enemy is healed, heals this champion by 20% of that heal. 

I always use Ronda and her A2 as fast as possible against UDK to shut down his passives.

all great suggestions guys.  I think I recently cracked the UDK code.  There was sort of a critical mass damage threshold I needed, and that came with the elhain path and blessings.  Before this event, the affinity of UDK was a super big problem, as my DPS/ADCs were blue.  I tried also using some green DPS, like soulbond bowyer, but OTHER people's blue DPS would hit them too hard.  

Once I got the blessings though for my most powerful hero, my starter Elhain, the Dark blessing started proccing a lot and doing some serious damage that ignored defense.  This wasn't possible before for me, even with warmaiden and spirit host buffing.  

I'm mostly F2P, have only spent like 15 bucks and want to keep it real low for the gaming experience, so this game has been really interesting learning to adapt to much stronger accounts.