"Can you lend me some eggs?"
Translation:Mi puoi prestare qualche uovo?
This is the best answer I have found. Also scroll down and read the comments after the article; there are a lot of good questions and useful answers. https://blogs.transparent.com/italian/qualche-alcuni-o-dei/
Yes. Just for info, some other nouns that change gender between singular and plural are: il lenzuolo -> le lenzuola (the bedsheet / bedsheets); il braccio -> le braccia (the arm / arms); il labbro -> le labbra (the lip / lips); il ciglio -> le ciglia (the eyelash / eyelashes); il ginocchio -> le ginocchia (the knee / knees).
The point is, when you say "can you give me some eggs" it implies you won't give them back, noth the ones you want and not others you'd buy for them. When saying "can I borrow", you imply that you will get the person you are borrowing them from new ones some time later. Of course it's very unlikely that someone will borrow eggs and give exactly the same ones back.
Well... what about "can you lend me a hand?" You're neither giving it nor taking it back. "Lending" and "borrowing" are idiomatic and now, in English and one supposes in Italian too, interchangeable with "giving" when asking for something to be immediately consumed (e.g. butter, milk, eggs, firewood, gas for your lawnmower). But lend in a different context means something different (e.g. a hundred dollars, your car). It seems with Italian you have to accept double-negatives and a whole lot of other things that may or may not be found in English. And practice.
No. The 'clitic' pronouns always have to 'attach' the conjugated verb (either by coming before it or by forming a single word with it). So 'Mi puoi prestare' is fine (because it's coming before the conjugated verb) and 'Puoi prestarmi' is fine (because it's forming a single word with it), but 'Puoi mi prestare' is wrong.