Is であって a -て form of the copula である and used for chaining, or it has a special meaning in the following examples?
どこの出身{しゅっしん}であっても問題{もんだい}ではない。It doesn't matter where he is from.
私{わたし}は彼女{かのじょ}が幸{しあわ}せであってほしい。I wish her happiness.
どこの出身であっても問題ではない。=どこの出身である(where he is from)+としても(even though)+問題ではない(it doesn't matter)。
「XXXであっても」 = 「XXXであるとしても」 = even though XXX is true.
It doesn't matter wherever he is from.
私は彼女が幸せであってほしい。= 彼女が幸せである(she is happy)+事{こと}を(that)+私は願{ねが}う(I hope)。
「であってほしい」= 「であることを願う」(We say "であることを願う," but don't say "であることをほしい")
I'm entirely not sure whether she is happy or not. (She is still one of my best friends, so) I strongly hope that she is happy.
Note: After clarification by user virmaior, the answer has been altered greatly. Older answer is below the new for reference purposes.
virmaior, thanks for clarification. Your specific question at this point in time is what prohibits 「幸せであって欲しい」 from being misinterpreted as 「幸せ出会って欲しい」. The answer in this case is multilayered.
First, the sentence contains kanji but the specific place you are inquiring about is in hiragana, and also already grammatically correct as is. There would be no reason to read it as 「出会う」.
The second is a simple grammar rule which you are most likely to be already familiar with. To 「会う」 or "meet" something in Japanese requires a particle indicating the object of the action, which would in this case be either 「に」 or 「と」. Since the nuances between the two particles are somewhat difference in this case, with 「と」 implying some sort of interaction, I would say 「に」 is a better choice. So, in order for 「彼女」 to 「出会う」 with 「幸せ」, the sentence would have to read thusly:
「彼女が幸せに出会って欲しい」
Because the critical particle is not there, and the sentence in itself is already grammatically correct, I see very little reason for anyone to misinterpret that particular part of the sentence to mean "meet" as opposed to "be".
Old Answer
Note: This answer is in response to a bounty posted by user virmaior and only addresses the second example given by the OP.
As you probably already know,「である」 is basically a more formal way of describing a status. It's the equivalent to "~ is". Here's a link with more information on how to use 「である」.
Example: "The sky is blue." --> 「空は青である。」
As you are also probably familiar, the て-form is often used to connect two verbs.
So, in the example you gave, 「彼女が幸せであってほしい」, the て-form serves to connect the first verb, 「である」, with the second verb, 「ほしい」.
Just simply directly translate it and you get "I want(ほしい) her to be(である) happy." Nuance-wise, a better translation would probably be closer to "I really hope that she is happy (right now).", where the content in the parentheses was added by me for effect to help with understanding the nuance.
Please note that using 「である」 isn't really for everyday speech. You'll be more likely to find it in written Japanese such as literature, poems, or song lyrics.
Feel free to google 「幸せである」 and you will get millions of results, including songs with titles that include that phrase.
I think Xuanrui Qi 's answer is correct. It's te-form of である. It's not 出会って here!
Weblio辞書 says:
「である」に接続助詞「て」が付いた形。
It's a form what "である" belonged "て" .
て is attached when a word becomes a conjugated form. So it's te-form.
I suppose であって does not has a special meaning.
どこの出身でも問題ではない.
Second sentence sounds a little weird because I hear幸せになってほしい
in my head as sounding more natural