Learn English – Meaning of “attached to material”

In the second paragraph ("I want to see the world, and that I will!") the meaning is: "I am very determined to do much travel and see the world." The "and that I will!" fragment could be re-written as "and I am very certain that I can ensure that this will occur through my efforts!"

In the last paragraph ("who can appreciate sarcasm and dish it right back") the meaning is: "I like the use of sarcasm and I use it myself, particularly when directed at me."

The basic construction as [adjective] as [expletive] essentially extends more literal / transparently metaphorical usages such as as good as gold, as hard as nails, as nice as pie.

Additional to OP's cited hell usage there's the slightly more euphemistic...

He's as mad as heck
...and the more explicitly coarse...
He's angry as fuck
(It was as) dark as buggery (this one's far from common, particularly in AmE)

But note that not many "expletives" can be used in this way. Despite what the prudes say, people who swear a lot don't necessarily do this because they have limited command of the language. The "rules" of swearing are often extremely precise - unsurprisingly, since one of its more important functions is to easily distinguish "in-group" from "out-group" speakers.

In the coarser versions, there's usually no specific semantic content to the particular expletive. They're all just used to convey emphasis (and/or prosody/rhyme in OP's example).

If anyone can suggest any other expletives that can be used in this pattern, please add a comment.