How Summoning normally works is that a clone of a Servant is made from the Throne of Heroes and this Clone, and their memories/experience/changes in nature (ie. corruption) are discarded so the original remains the same.
with Arturia's case she made her contract with the World before she died to obtain the Holy Grail in exchange to becoming a Heroic Spirit as such she's not being summoned from the Throne of Heroes but from the moment before her death. When Saber's nature as a Servant is discovered the Visual Novel shows a couple of images to explain how her contract works
the first image shows how Saber will return to the point in time before her death after each attempt at getting the Grail. the second image is what will happen when she completes her contract in which when she completes it she'll proceed to her death rather than before she died before then going to the Throne of Heroes.
In regards to her memories in Fate/Stay Night, regarding her memories of the 4th War she does have them as on her Wikia page under her Role of Fate/Zero
With the Grail gone and unable to maintain her form, Saber is sent back to the battlefield of Camlann, as she remembers the words of Lancelot and Rider.
Source: Saber (Fate/Stay Night) - Role - Fate/Zero (Second Last paragraph)
also in the Heaven's Feel Route after their run in with Ilya and Beserker, Shirou is confused as to Ilya's hostility to him. Saber contemplates as to whether to explain this to Shirou but instead telling him to seek out Kotomine despite wanting to have as little contact with him as possible due her own personal dislike for her former Enemy Master. before Shirou enters the church (leaving Saber outside) she suggests not to reveal that she's been summoned again.
while is a different route which -Last Episode- wont occur one can speculate that in the Fate Route she stayed outside for the same reason (even though at this point it had yet to be revealed who she is) as such if she remember Kotomine then she remember's Lancelot's and Rider's words. but ofcause as apart of her "dream" it wouldn't be a fond part as it involved Kiritsugu forcing her to destroy the Grail with his remaining Command Spells
As for what other memories she would have in -Last Episode- we can assume that it's only what she would remember by the end of the Fate Route (including her previous attempts) as since in the Fate Route her contract is terminated due to it being her choice to destroy the manifested Holy Grail and accepting her appointment as King any further attempts would not be known to her.
However because the Nasuverse is a huge multiverse with alternate timelines which is all connected via the use of The Second Magic the ending of the Fate Route would create it's own timeline, as such the ending of the other Routes would create their own timelines including:
- One where her her corruption in Heaven's Feel is carried to future attempts at the Grail
- One where she lives a full shoujo ai/yuri life with Rin after the Good Ending of Unlimited Blade Works
- One where she continues going for the Grail after the True end of Unlimited Blade Works (as it was not the complete Grail that was summoned)
- One unknown ending of Fate/Stay Night which leads to Fate/Hollow Ataraxia in which she was corrupted yet the Greater Grail wasn't shut down/destroyed by Shirou or Ilya
since the Throne of Heroes is disconnected from the rest of the universe allowing the summoning of "heroes" from other timelines (Archer in Fate/Stay Night is the perfect example) there is a high probability that an Arturia would end up there. however since she would have memories of previous Holy Grail Wars/Attempts probably the only way to tell you have summoned Arturia herself or a clone is to ask if she ever got a Holy Grail before.
as a final note, since Fate/Labyrinth was made well after Fate/Stay Night and without knowing when in Arturia's own timeline she would have shown up there (ie. would she have remembered Waver from the 4th War as Waver would remember her?) i would speculate that in the Fate Route she wouldn't have any memories of the events in Fate/Labyrinth.
