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Why are the lulav, hadassim and aravot bundled together? What's wrong with leaving them separated? Why not bundle the etrog with them? Why is it separate?
Are there any hints / references in the these 3 must be bundled, but the etrog must be separate?
To answer why the lulav, hadassim and aravot are bound, see e.g. Sukkah 33a:
דתניא לולב בין אגוד בין שאינו אגוד כשר ר' יהודה אומר אגוד כשר שאינו אגוד פסול מאי טעמא דר' יהודה יליף לקיחה לקיחה מאגודת אזוב כתיב הכא (ויקרא כג, מ) ולקחתם לכם ביום הראשון וכתיב התם (שמות יב, כב) ולקחתם אגודת אזוב מה להלן אגודה אף כאן אגודה ורבנן לית להו לקיחה לקיחה מאן תנא להא דת"ר לולב מצוה לאוגדו ואם לא אגדו כשר מני אי רבי יהודה כי לא אגדו אמאי כשר אי רבנן מאי מצוה קא עביד לעולם רבנן ומצוה משום (שמות טו, ב) זה אלי ואנוהו:
[I]t has been taught: A lulab, whether [the other prescribed species were] bound with it or not, is valid. R. Judah says, If it is bound [with the others] it is valid; if it is unbound, it is invalid. What is the reason of R. Judah? — He deduces it from the word ‘take’ [which occurs here and with] the bundle of hyssop. It is written here, And ye shall take on the first day, and there it is written And ye shall take a bundle of hyssop. Just as there [it must be] a bundle, so here also [it must be] a bundle. And the Rabbis? - They make no deduction from the mention of the word ‘take’ in the two passages. Who is it that learned that which our Rabbis have taught: It is a pious deed to bind the lulab, but [even] if he did not bind it, it is valid? Now who is it? If R. Judah be suggested, why is it valid if he did not bind it? If the Rabbis are suggested, what pious deed does he perform? — It is in fact the Rabbis, and the pious deed spoken of is due to ‘This is my God and I will glorify Him’.
So the reason for binding is subject to a debate between tanna’im: R. Yehudah believes it to be an absolute requirement derived hermeneutically, whereas the other sages believe it to be the ideal way of performing the mitzvah in a beautiful manner.
Halachah follows the opinion of the majority of the sages; one should bind the lulav but one still fulfills the mitzvah even if all four species are picked up individually (see Shulchan Aruch Orach Chaim 651:1 and 12).
As to why the etrog is not bound together with the other three species, see Sukkah 34b:
תניא רבי ישמעאל אומר (ויקרא כג, מ) פרי עץ הדר אחד כפת תמרים אחד ענף עץ עבות שלשה ערבי נחל שתים ואפילו שנים קטומים ואחד שאינו קטום ר' טרפון אומר שלשה ואפי' שלשתן קטומים ר"ע אומר כשם שלולב אחד ואתרוג אחד כך הדס אחד וערבה אחת אמר לו ר' אליעזר יכול יהא אתרוג עמהן באגודה אחת אמרת וכי נאמר פרי עץ הדר וכפת תמרים והלא לא נאמר אלא כפת
It has been taught, R. Ishmael said, ‘The fruit of a goodly tree’ implies one; ‘Branches of palm-trees’ implies one; ‘boughs of thick trees’ implies three; ‘willows of the brook’ implies two, and even if two [of the myrtle-branches] have their tips broken off, and only one is whole [the wreath is valid]. R. Tarfon said, [There must be] three, [and they are valid] even if all have their tips broken off. R. Akiba said. Just as [it is necessary to have but] one palm-branch and one ethrog, so [it is necessary to have but] one myrtle-branch and one willow-branch. R. Eliezer said to him, If one should say that the ethrog should be bound with them in one bundle you can answer, Is it then written, ‘The fruit of a goodly tree and branches of palm-trees’? It says only, ‘The fruit of a goodly tree, branches of palm-trees’.
