With regards to the revive situation, if a mastery kills an enemy champ then the block revive doesn't kick in.  If Zavia has Giant Slayer or Warmaster then it is likely this would have proc'd and dealt the fatal damage.

With regards to the speed situation, it is likely masteries as well.  If the DPS has the mastery that gives extra speed on kills then they could end up being faster the next round

If your Zavia is on warmaster/giantslayer, if they are killed with this mastery, the "can not be revive" will not take effect. 

If enemy got killed because of Bulwark mastery, the "can not be revive" will also not take effect. 

As for your second query, we have to know your team comp and speeds, and your enemy team comp to verify if there is a bug

Another possibility for your second problem is that there is a Valkyrie on the enemy team. Valkyrie's passive reads:

Jealousy (Passive)
This Champion’s Turn Meter will be increased by 10% each time an enemy Champion places a buff. Enemy Champions will have their Turn Meters decreased by 10% for each buff they receive. 

This annoys me every time that I attack a Valk team with my team including Madame Serris. As you may know, Serris gets an automatic shield buff on her, so Valk's passive will reduce her turn meter at that point, which will often make the DPS get their turn before Serris can debuff. 

Regarding 1st thing - your explanation make sense but still is crazy- why to have some effect cancelled by mastery ? That means that any champ that have " enemy killed by skill cannot be revived" shouldnt have warmaster/giantslayer mastery?

Regarding 2nd thing- didnt know if Valkirie was on opposite team but I will look more closely 4 the future :)

Thx a lot guys for your explanations 

the effect doesn't get cancelled by the mastery, it just doesn't extend to it. the only time an issue like yours occurs is if the attack doesn't kill the opponent, but leaves them with low enough health that the damage from warmaster or giant slayer does.

When you kill the enemy - if you don't see the "Block Revive" scroll up - then it wasn't the skill that killed them (really annoying).  Regarding slower turnmeter going first - I had a similar issue -  until someone pointed out it may be because of Valkyrie's passive - which it was.

Today got same problem with slower champ going 1st and was no Valkirie on the oposite team :(

Are you sure the other champ is slower? What are the speeds of your champs?  Valk isn't only champ that can cut in, Yoshi of course is another :) Though you won't see much of him in classic or low level tag I would guess.  Astralon, Maulie, ... and others disrupt order from starting speed as well.  Also, if you are not speed tuned, your TM boost may only temporarily provide a visual that your slower champ is ahead in turn order but your faster opp champ will make up the difference and "cut back in".

Which champions were on the enemy team? And did you get hit, especially with a critical hit, before your champions took their turn? It could also be because of masteries on your team. 

That is fresh fight ( this morning)

Normal order ( my team for this fight) is Arbiter/Stag/Kreela/Astralon.

Enemy team : Dutches/MaShalled/Countess Lix/Inquisitor Shamael.

In this fight , order was Arbiter/Stag- with retaliation from Shamael( counterattack on Stag) / Astralon and only after arrive Kreela turn .

So enemy team had only 1 counter on Stag and still Kreela lost her position ( with no attack on her ay all) and attack the last.

What are the speeds of your champions? 

astralon's passive boosts his turn meter whenever an ally is hit, so shamael's attacks likely pushed him ahead of kreela.

Another  factor  which  can  mess  up  move  order  is  Speed  Aura  Leads.

If  your  heroes have  very  close  speeds  outside  the  battle,  The  Speed  Aura  boosting  speed  in  the  battle  can  sometimes cause  issues.

I think the most common reason is Cycle of Revenge. That causes your champ to boost TM if an ally receives a critical hit. Another mastery that might be kicking in is Timely Intervention, this one triggering when an ally drops below 20%. There's a few other masteries that affect TM as well, though to a lesser extent - Oppressor for example.

What speeds are you running? I think folks are asking to help check the speeds are tuned so that you don't easy get cut.

And krama's masteries there are a good list. If your sppeds aren't close enough, some of those masteries will get your cut for sure.