The Spanish for syrup, jarabe, comes from the same root as the English: the Persian/Arabic sharab, which means “a drink, or wine”.
The drastically different (at least superficially) words are explained by the sh- and related (such as, sy- ) sounds changing to the Arabic-sounding j- sound in Spanish — but not English.
Thus, the j-r-b of jarabe maps to the sy-r-p of syrup.
The Spanish mancha (“spot” or “stain”) comes from the Latin for the same, macula.
From the Latin macula, we get the English… immaculate — which literally means (knowing the negation prefix of im-) “without a stain.” So the immaculate conception truly was perfect!
How this sound changed was interesting: often Latin words with a ct- or cl- or other hard letters after a c- sound turn into a suave ch in Spanish. For a distant example, see duct and ducha, or nocturnal and noche. (The ct- is much more common than the cl-, but they’re cousins!) Thus, we can see the m-ch of mancha mapping to the (im-)m-cl of immaculate.
The usual Spanish word for “name”, nombre, is very closely related to the English word nominal, in an interesting way. Not only does nominally mean “relating to the name”, but there is an interesting etymological pattern between the words.
Latin words with an m-n sound usually turned the m-n into an mbr sound as Latin evolved into Spanish. Thus, we see curious patterns like hominem becoming hombre, and famine and hambre being closely linked.
The same pattern applies here. The Latin nominalis turned into the Spanish nombre and the English nominal — thus the n-m-n of nominal maps exactly to the n-mbr of nombre!
Daño, Spanish for “damage”, comes from the Latin for the same: damnum. From the same root we get both the English condemn and damn. But what happened to that missing ‘m’?
Interestingly, the Latin m-n sound tended to turn into a ñ sound in Spanish. This explains how autumn became otoño, for example.
We can still see this pattern preserved in the perfect mapping of d-ñ in daño to the d-mn of damn, and the same with condemn.
From the same root we also get the English indemnity, as well as damage itself, although the final -n was lost because damage entered English via French.
We can see the parallel but between daño, condemn, damage, and damnum — but how did it come to mean the formerly-vulgar, damn? Think of damn in the old sense of, sentencing someone for a crime they did: you are condemned to hell. A whole slew of English insults come from this same concept, including the word hell itself!
The English foot comes from the Indo-European root *ped. Think pedal.
Interestingly, the “p” sound consistently transformed into an “f” in the Germanic languages — but remained a “p” in the Latinate languages.
This is why, foot is equivalent to pie.
Other examples of this pattern include father and padre, and the English far is from the same root as the Latin per.