"This is the longest snake that I have seen."
Translation:To najdłuższy wąż, jakiego widziałam.
What is the grammar behind "jakiego" and how is it different from the "który, etc." constructions?
If you had a simple "I've seen a long snake", then it would be easy to see that the verb "widzieć" needs Accusative: Widziałem długiego węża. So similarly but from a different side, the sentence uses Accusative as well.
A bigger problem is that for masculine gender, the nouns are divided into animate and inanimate ones, with a lot of them (especially food and beverages) being grammatically 'animate' for no reason at all. Anyway, for inanimate ones the Accusative is the same as Nominative, so if it was a long table, then it would be "Widziałem długi stół".
The difference between "jaki" and "który" is not that easy to explain. It mostly lies in in that "który" suggests a finite set of options. For example "What is your favourite colour" will rather be translated as "Jaki jest twój ulubiony kolor", although you could also say for example "Który kolor lubisz najbardziej" (Which colour you like the most), and then it suggests there is a closed set of options to choose from. "Jaki" is also often translated as "what kind of". (Jaki chleb lubisz najbardziej = What kind of bread do you like the most).
In this sentence, "którego" wouldn't work, although I don't know how to explain why. But you could add another sentence: "But the snake I saw in 1972 was almost that long as this one" and that would rather use "którego": "Ale wąż którego widziałem w 1972 był prawie tak samo długi jak ten". I don't know if that's helpful or rather more confusing, but I'll hope for the first option ;)
That sounds weird. "zobaczyłem" is of course "I have seen", but one time, and sounds like a short time. If it is "I have ever seen", I'd say only "widzieć" works.