I prefer
This is the best performance I have ever seen.
over
This is the best performance I ever saw.
They mean the same thing (namely, that the person saying it witnessed the best performance thus far in their life) unless context implies otherwise.
This is the best performance I will ever see.
The sentence means they will never see a better performance; it's impossible for another performance taking place in the future to be better than this one.
Firstly, note that the best gift [that] I [have] ever have isn't a "sentence" - it's a "noun phrase" (within which the "head noun" is gift). Also note that it's perfect okay to include or omit either/both the "relativiser" that and the "auxiliary verb" have, and this has no effect on the meaning (it's entirely a stylistic choice).
BUT the second instance of have isn't an auxiliary. It's a normal verb usage, with the meaning get, obtain, acquire, receive,... So our choice is between...
1: This is the best gift I ever get
2: This is the best gift I ever got
3: This is the best gift I will ever get
In all those examples, the optional word ever provides emphasis (drawing attention to the fact that I never get or got or will get any gift better than this on any occasions whatsoever).
In most contexts, Past Tense (best I ever had) is the correct choice (in which case you're not necessarily ruling out the possibility of getting an even better gift in the future). You're saying that at no time in the past did you ever have anything better.
But note that Present Tense (best I ever have) doesn't exactly refer to present = now = time of speaking. It's the "timeless" use of the verb form, implying "never at all" (in the Past, Present, OR Future). And that's probably not the intended meaning.
It's possible to be even more emphatic by using could instead of will for the "future" reference in #3 above...
4: This is the best gift I could ever get
(there never was and never could be a better gift)
...and it's possible, though a bit clunky, to use that form for the "Past up until Present" context...
5: This is the best gift I could ever have got
(no past or current gift is better, but feasibly there might be a better future gift)
Best Answer
The sentence is ungrammatical because of the presence of "ever". "Ever" belongs to a group of words called "negative polarity items".
The unusual thing about negative polarity items is that they can only appear when there is some suggestion of doubt or unreality in the sentence.
Here are a few of the situations where you can use "ever":
There are a couple of other situations. See this answer on English Language & Usage for more detail.
Another negative polarity item that often causes difficulty is "any".