Lancer always dying is a joke in carnival phantasm, the reason why he dies is or who kills him is of little importance. For example, in one of the first episodes of carnival phantasm when the cat characters are talking with the TV on we hear about a man in blue thighs being killed in a car accident. It is of course Lancer, and he just died for no reason ...
That arm could be the arm of Kiritsugu Emiya. In the picture the characters are connected to thier masters. The masters of Saber would be Shirou Emiya and Kiritsugu Emiya.
It could also be the arm of Irisviel van Einzbern, who wasn't the real master of Saber but some sort of stand-in, while Kiritsugu was doing his dirty work.
There's a zerochan image suggesting that it's Irisviel:
However, it credits a Pixiv user so chances are that it ain't official. Nevertheless, there are some bases for such an assumption:
Irisviel has a connection to Saber (being the stand-in Master during Fate/Zero)
the arm looks feminine
Despite Logan M's comment Fate/Zero characters do appear in the ...
I believe the one on the far left is Kariya Matou from Fate/Zero,
the one next to Chikagi is Rani VIII from Fate/Extra (it's a bit hard to see as reface is mostly obscure, but the clothing and skin color matches),
and the one in front of Miyako is Assassin (Li Shuwen), also from Fate/Extra (the wardrobe practically gives it away).
I am not sure if there's a superstition in the Japanese culture or just among the animators but according here,
In a lot of anime, a character (usually the protagonist) will show up
in the opening or ending credits, running along while remaining on a
fixed spot on-screen. The character could be running the whole time,
or start out walking slowly and ...
This is an interesting question, but without an official source to confirm the answers, they can only remain as speculations.
If you pay attention to the forearm of the hidden character, it is not covered in sleeves, nor is it decorated with anything, like a wrist band, so Kiritsugu is out. Saber's friendly gesture towards the unknown person shows a ...