Hey Giraffes! Welcome to the forum.
Words like "burning" or "drowning" will likely be added later to their respective categories (for example words starting with trt will be related to fire). Until then:
Remembering that Sarus has a limited vocabulary with a mission to suppress synonyms or extraneous words, to say "today is windy", you literally say "today is wind" (dms t frf - this can also be literally translated to say 'today wind-ing', essentially the same thing). An even shorter way would be to say "wind today" (frf dms), which means "windy today", unless context states otherwise.
Therefore, to say that something is burning, you simply say it "is fire" (t trt), or even "has fire" (mrr trt). If someone said to you "his hat is fire" (df ssmt t trt), chances are you'd understand.. the concept is simple and you would more than likely picture a hat on fire.. i.e. burning hat. I understand that actual burning is different to simply having fire, so where necessary you could get creative, perhaps by saying it's "fire-eaten" (trt tt fdt) or "dying in fire" (t tsr sdt trt).
For coming up with animal names, bear in mind you don't really need to add the word 'animal' (lrd) if you don't want to. In the same way that we know 'yellow belly' means a type of fish, or 'red back' is a type of spider, you could just say "long neck" (frd rtst). Add "with fire" (r trt) and you have a burning giraffe

By the way, you might not have noticed but animals are split into sub categories:
frd rtst lrd(r) = long neck animal(s)
frd rtst lrdd = long neck bird
frd rtst lrdm = long neck fish
frd rtst lrdf = long neck reptile
frd rtst lrds = long neck amphibian
frd rtst lrdl = long neck insect
frd rtst lrdt = long neck mammal
At the end of the day, Sarus is yours to experiment with. If context sells an idea, great.. if you can get a simple idea across with a few short, simple Sarus words, even better. For me, getting that ideal short phrase is half the fun
