No Fhasan, you should use one only, for example 'A tiger can jump a distance of about 30-35 feet. ' or 'A tiger can cross a length (distance) of about 30-35 feet.' OR PERHAPS ' A tiger can jump across a stream 30-35 feet wide.'
I think, you can drop the "and" because here there are two full imperatives: Go! Get it! (also: "Go and get it!")
In the sentence "A tiger can jump cross a length of about 30-35 feet." the 'and' can't be dropped because the action expressed by the verb wouldn't be completed then. It has to be "A tiger can jump and cross...".
Nope, "let" is a weird verb because it can take over or imply a kind of modal meaning in special cases, just a bit like the common usual Modal helping verbs which are always followed by an infinitive.