The fire got named after him. In fact, either Mitsuha or Yotsuha commented on this way back in the scene where they were making the 組紐. They say something along the lines of “poor guy having a fire named after him and only being remembered for that”.
Side note: Earlier in this section, Taki (in Mitsuha’s body) made it clear he didn’t know this name. But grandma didn’t call “her” out for this? Hmm. And then with all that ムスビ talk about the interconnectedness of people and things, I kinda get the feeling she can sort of sense what’s going on with Mitsuha, no? I haven’t seen the movie, so don’t spoil it please. Just making the observation!
にせにゃいかん
This was tricky. I mean, it was obvious from context what it meant, but until I dug into it, I couldn’t explain exactly what was happening grammatically. According to a post I found on HiNative (where, by the way, many Tokyo natives appeared to be somewhat confused by this line themselves):
せにゃ/しなくちゃ
いかんよ/いけないよ
引き換えにしなくちゃいけないよ
This makes perfect sense to me.
あんたたち
あんた does sound condescending if you use it towards someone who is ostensibly “on the same level” as you in terms of age/rank/whatever. But, she’s their grandmother, so she’s well within her right to refer to her grandchildren in such a way. It doesn’t sound condescending or rude in this case. More like “hey kids listen up”, which your grandma can totally say to you. It’s kind of hard to explain, but I hope you get the idea.
渡り終えてから…
渡る: To cross
終える: To finish
Hence; 渡り終える = to finish crossing
〜てから: After
言わないで: Don’t say
All together: Don’t say that after we’ve crossed!
In other words: you could have warned us before we crossed into this “other world” that we were going to have to give up our most precious possession in order to get back!
Hopefully this helps! Also, I’m hardly an expert at any of this myself, so please someone feel free to jump in and correct me if I’m accidentally leading people astray! 
Edit: Just added some extra details/observations.
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