We know Avrohom interrupted speaking to God to invite guests – from here our sages deduce that inviting guests is greater than receiving the Divine – but as inviting guests may incur waste of Torah study, or Lashoin hara – nonetheless..
Oirech (guest) is Oir / Ches – the light of Ches which refers to the world to come, for s/he who invites guests, receives the world to come.
The guest brings Torah to the host – according to the caliber of the guest, so is the Torah that is revealed to the host.
Avrohom told Sara, hurry prepare three “pounds” of flour, and she took from the best – from here our sages deduce, that a woman is “cheap” with guests – the question is obvious (for she did from the best – while Avrohom said regular) so the Baal Shem Tov gave an example- once there was a lion who told his cubs, “we are the strongest of the animals” – so the cubs confidently strode to see the world – they came to an abandon palace and there they saw all types of images of animals- they also saw Shimshoin Hagibor tearing a lion as if it was a goat – terrified they ran back to their father… – “actually this proves the point… – for it shows that one person was capable of such a feat, hence it is being highlighted…” – similarly Sara was very righteous (hence she gave unstintingly.)
The Name אלד is good for a woman giving birth by concentrating that the א represents Chochmah and Binah – the ל the three pillars (I think this means right, left, center) and ד which is the Shechina, and one should have in mind to draw down from above to below.