Learn English – Is “fillet” a different word in “salmon fillet” than in “leather fillet”

All of the words you provide (limb, thumb, crumb) are listed in my local dictionary without a b sound. Things seem basically the same with suffixes (i.e. thumbed has no b sound).

Crumbled is is a completely different word and receives the pronunciation typical for "mble": thimble, tremble, fumble, etc.

It is true that crumb and crumble have common origins:

crumb - O.E. cruma "crumb, fragment," from a W.Gmc. root of obscure origin (cf. M.Du. crume, Du. kruim, Ger. krume).

crumble - late 15c., kremelen, from O.E. _*crymelan_, presumed frequentative of gecrymman "to break into crumbs," from cruma (see crumb).

The "b" in each word appeared later (mid-15c for crumb and 16c for crumble). Given the typical pronunciation of the "mb" and "mble" it isn't surprising that these words are treated the same. Why they received a "b" at all is a little vague from the notes in the above link.

Digging deeper I found Anatoly Liberman who gave a more thorough explanation:

The words thumb, numb, and dumb have unetymological mb in spelling, though they do not end in l. Why do they? In principle, the story begins in late Middle English. At that time, consonantal groups were often simplified. Solemn and column are now pronounced without n. In the speech of some people kiln is homophonous with kill, g is always mute in diaphragm, phlegm, and so forth. Because of the simplification, lamb was fleeced of its historical final b; today b is retained in spelling but not in pronunciation. The same happened to jamb, plumb, and tomb (borrowed words), along with womb (Old Engl. wamba “belly”; compare Wamba, the name of Cedric’s “fool” in Ivanhoe) and climb (Old Engl. climban).

As long as the simplification of consonantal groups remained an active force, literate people felt uncertain when to write m, as opposed to mb, and began to add b to m gratuitously, a mistake (here, reverse spelling) called hypercorrection. This accounts for the modern forms limb and crumb.

The rest of that article is extremely fascinating and highly recommended. Also relevant are words like limber, timber, combine which most certainly pronounce the b despite the "mb". So are other cases of a silent "b": debt, subtle, etc.

Alas, both words most probably do not come from the same root. So far as we know, their identical spelling is completely accidental. They were already spelled the same more than two thousand years ago by the Romans.

Our word German comes from Latin Germanus, first attested in Caesar, which was used to describe the Germanic tribes by the Romans. According to the Oxford English Dictionary (2nd ed.), it may be of Celtic origin, as a name used by the Celts to designate their neighbours; but there appears to be no consensus yet.

The word germane comes from Latin germanus (adjective "related, relative", noun "brother") This comes from the Proto-Indo-European root *gen-, which means something like "give birth". Our word germ, from Latin germen, "sprout", is from the same root, as is genetic, through Greek genesis, "birth".