I don't think "viszlát" and the verb "visz" (carry) are closely related. "Viszont" means 'again' and "vissza" means 'back' (like in turn back), these are related. "Viszontlátásra" means literally "on seeing (us) again", "viszlát" is an informal abbreviation of it. As Hungarian people expect and appreciate politeness, "viszlát" should be avoided in all formal situations and when talking to elderly people. But of course feel free to answer a "viszlát" with a "viszlát".
It may be hard to hear at first, but believe me that it can be heard. In fact, some of these are common mispronunciations that sound sloppy if someone native uses them.
"Mit csinálsz?" is a good example. You can sometimes hear people saying it as "Micsinász?" (both the t and the l missing), sounds careless or uneducated or maybe like an accent.
"Elnézést" is similar, normally people use the l, but it only changes the tongue location during the second half of the "e" (touches the teeth), as Mrton said. If you skip it, it sounds sloppy but is understood.
I think you are referring to something general about how consonants work in Hungarian. The main rule is that consonants following each other will merge -
as long as they can. For l, this means you may start pronouncing the next consonant (n and sz in your case) without a break or stop. The sound all comes from putting your tongue in the right position (alveolar ridge or upper teeth), the rest is "shadowed" by the next consonant.
So at the end of the day, I kinda get you but I think it could be noticed if someone actually skipped l in these words. Two more things, if I may. It's "csinálsz", "cz" doesn't exist anymore as a digraph (it used to be what is currently "c", till like 100 years ago). Also, I don't find el->é any plausible. Watch out, this is not Czech/Slovak, é is NOT a lengthened e, in fact, there is no lengthened e in Hungarian. (I'd probably go with "eenézést" if I really wanted to use Hungarian orthography for that... but really, I just want to make sure you don't mistake é for a long e.)