I am using this edition of the Fabulae Divales as a basis for my below answer.
In general, Latin prefers to link clauses that would often be independent in English: propter quod, quam ob rem, qua ratione are examples of causal linking.
Using the relative pronoun with et (or, even more commonly, autem or enim) has many precedents: it links two otherwise separate clauses.
In eo perpetua canalis, in quam et cibus imponitur iis et immittitur aqua (Varro, De Agri Cultura, III.11)
There is a perpetual channel in it, and in it [=this channel] food is placed for them and water is allowed in.
in tali tantaque
This phrase is fairly common and means something like "of such a great kind". At least in my own head, I see it as a kind of hendiadys ("use of two words connected by a conjunction, instead of subordinating one to the other, to express a single complex idea").
Here is one classical example of its usage:
atque hoc non solum in te, tali et tanto viro, satis habebit (Letters to Atticus)
tantaque throws me for a bit of a loop, but I am confident that it is a typo. The only feminine words it could agree with in context are ancilla and lucerna, but neither works: tanta ancilla is rather mean, and there is no way to make tanta lucerna work with the rest of the sentence.
I read through the (otherwise delightful) Latin of the tale and noticed some other small errors such as:
- pg. 9: qaum instead of quum (= cum)
- pg. 12: nolli timere instead of noli timere
So, in the absence of better suggestions, I am willing to chalk this up to bad copy-editing or type-setting.
My proposed full translation (keeping the narrative present tense):
Regia Filia jocum dignata mittit ancillam cum lucerna, quam et magus erga novam perlibenter emutavit, quod satis novit in tali tantaque Aladdini palatio haud duas lucernas antiquas reperiri posse.
The Princess, consenting to the joke, sends her handmaid with the lamp, and the magician gladly exchanged it for a new one, for he knows well enough that two old lamps can hardly be found in such a great palace as Aladdin's.