Was the translation for "name-nal" not already name's place? And now "name-ék-nal" is the same?
The his friends/family thing is not in there?
Would "&company" be eventually a slightly awkward but fitting translation for -ék- here?
It is a bit ambiguous.
"name-ék" means "name" plus family/friends/company. It depends on context, situation, etc.
Now, if you add "-nál"/"-nél", that is their place.
"Lászlónál" - at László's place
"Lászlóéknál" - at László and company's place
But the default understanding is that László lives with his family. So, "Lászlóéknál" is most likely László's family's place.
Of course, László could be sharing a rental apartment with some friends. In that case, that is László and friends' place.
So, the difference between "Lászlónál" and "Lászlóéknál" is mostly that between singular and plural. Using the former, László probably lives alone. Using the latter, László probably lives with his family, friends, etc. Note the word "probably".
So, you are correct in your assumptions.
But, in English, one usually does not make this distinction. I can say "at my place/home", and I could be referring to the family mansion.
So -ék is kind of like a plural suffix, with a clear meaning in context but no perfect English equivalent.
I hope -é follows too, since that seems more important
There is a theory that "-ék" comes from a possessive suffix. It means something like "László's people". And then context may tell us who those people are.
I am not sure what you mean by your second sentence. Care to elaborate?
Just that, -é = belongs to, is hopefully a part of the coming "to have" lesson. It seems more important to me than something I can barely grasp since it does not really exist in English (and German as far as I am aware)
Well, "-é" is just the third person singular possessive suffix for "belongs to", so surely you will come across it.
But you might also want to learn "-ék" as it is a very commonly used form in Hungarian.
As a side note, a similar solution also exists in Turkish, but they simply use the plural suffix. So, it would be literally "Lászlók" in Hungarian. Instead, Hungarian also adds a pinch of possessiveness to it.
Colloquial English does have a suitably vague equivalent:
"Lászlónál" - at László's
"Lászlóéknál" - at the Lászlós'
Adding the definite article makes the plural clear without explaining the living arrangement. No further nouns is needed, as house, flat or whatever their living arrangement is is understood. The Lazlos could be a married couple, siblings, a family etc.
I guess the only difference is that the plural form is not really used with first names, or singular relations, is it?
"At the Steves'", "at the Susans'", "at my mothers'", sounds a bit weird.