3 problems regarding lancer in fate/stay night (anime)

[Flip Flapper]

so i watched episode 22 of the original fate/stay night anime today and..... there are 3 big things i want to adress in this episode, and before i start i want to say that lancer was my favorite servant in the franchise, especially what we have seen of his counterpart in prototype and since i was kidna introduced to the franchise trough prototype and carnival phantasm were lancer apears a lot in tha tprobably helped me to get into the franchsie and is all the more reason for me to like lancer

also SPOILERS

that said this episode had some stupid things regarding him (IMO)

1. Saber not knowing who lancer from the 4th grail war was.....
even if this oculd be said to be ebcuse of ret-cons she did fight lancer 2 times and fought alongisde him at least 2 times in the 4th grail war and even if that was becuse of retcons she should have known who it was since she should have at least seen him, in fact she recognized him really quickly upon learning his abilities, Diarmuid U Dubhine (Diarmuid of the love spot) and she also recognizes lancer in the 5th grail war as Cu Chullain, in this episod ewhen Rin theorize that Lancer could be a survivor from the 4th grail war saber agrees that it is the most likely thing.

2. Lancer´s motives
Why did he betray Kotomine? He was fine with Kotomine cheating, killing people and a shit ton of other things but in this series (it may have been for different reasons like some spoilery ones i wont mention here wich are connected to Shirou´s backstory) but what made him betray him was that he had Gilgamesh AND Lancer as servants..... what!? why is that so bad if he already cheats?

3. Battle continuation
one of lancers skills is battle continuation wich lets him continue to fight after he should die from injuries, he gets impaled by the caladbolg and then dies immediatly here, i know he is supposedly weak against it... when it is wielded by someone from Ulster when here it was thrown by Gilgamesh who is obviously not from Ulster yet Lancer did not activate battle continuation here, also Shirou and Saber didnt run away from the chapel like they should and instead simply out of it and staretd patching Shirou up in the graveyard...... you do know Gilgamesh will probably see you from the entrance to the Church right?

just some things that bugged me, i may have missed something becuse of being tired right now but either way these are my thoughts on these things