What modern language is Trigedasleng based on, or most closely related to? Does it have the same basic family as any of our modern/past languages or is it completely made from scratch?

English. It is intended to be evolved from modern English. And it is. Every word of it comes from English. It’s also really, REALLY close to modern, colloquial, American English. Like, this literally is English:

Ha yu na hit em op?

In both English and Trigedasleng it means “How are you going to meet up with him?” It’s just that in English you’d write it:

How you ‘na hit ‘em up?

There’s been very minimal phonological change from modern colloquial American English to Trigedasleng; a little bit of grammatical innovation; and a lot of semantic change (basically taboo replacement, in a weird way). It’s by no means trying to disguise itself. It’s proudly and enthusiastically proclaiming its American Englishness. If languages were birds, this would be Trigedasleng:

If circumstances were such that there were no other survivors in The 100, the name of the language would probably just be English. Well. That is until they rebuilt civilization and met up with other large groups of English speakers, like on the West Coast, in the Midwest, in the South, etc. They might’ve changed enough that the languages would be unintelligible. No way to know, though, at present. Maybe someday, if the show gets there. We’ll see!