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I have noticed that there are letters embedded in other letters once pronounced.

I noticed that in these words:

Numb: b is silent but when you finish pronouncing the word with M letter, lips will be closed, whenever you open them again the letter B comes

Try that, say Num (without B) once finish lips will be closed.
Open lips, then you can hear a soft B when lips got open

Thomson: similarly after finishing the first part Thom, then start saying the next part, you can feel P in between making it sounds like Thompson.

Jail: it will sound like Djail.

Are there any other letters that have any other letters embedded in it?

The most prominent example of a letter that represents two sounds in English is X, which represents the clusters /ks/ or /gz/ in many words. That is entirely a matter of spelling, though, whereas your examples involve more interesting theoretical issues.

Each of your examples is somewhat different from the others.

• For jail, what's going on is that the "j-sound" is not a single pure consonant sound: it starts out like the [d] sound and ends like the [ʒ] sound found in the middle of a word like measure. Such "impure" consonant sounds are called "affricates" in linguistics terminology. The English sound system contains two affricate sounds, the j-sound of "jail" and the ch-sound of "choose". Other languages may have more or less; for example, [ts] is fairly frequently found as an affricate sound, but it's not considered to be one in English because it seems to behave more like a consonant cluster than like a single consonant sound.




• For numb, what's going on is that [m] and [b] are phonetically similar sounds: they're both pronounced with the lips in the same position (rounded and close together, called "bilabial" in lingustics terminology). The difference is that [m] is a "nasal" consonant, while [b] is an "oral stop". English speakers don't actually pronounce the end of numb any differently from the end of sum, and neither typically contains an oral stop [b]. If you make an especial effort to release the [m] at the end, I guess you might produce a sound that you hear as "b", but this isn't a usual feature of the pronunciation of numb. Likewise, despite the spelling, words ending in the letters "ng" usually don't contain any actual oral stop [g], just a nasal sound [ŋ] that is produced in the same position in the mouth.




• For Thomson, what's going on is that it's physically difficult to transition directly from the [m] sound to the [s] sound, so English speakers often produce another sound in between: [p], which is a "voiceless" bilabial stop (made with the same lip-shape as m or b). These kind of transitions commonly arise between a nasal consonant and a following voiceless fricative, as in [n(t)s], [m(p)s], [m(p)f], [n(t)θ], [m(p)θ], [ŋ(k)θ]. They may be described phonologically using the terms "epenthesis" or "epenthetic consonant".

A common example of sounds that "contain other sounds" that you haven't mentioned is diphthongs: even though the vowel in the first syllable of a word like "riding" is written with the single letter I, it is pronounced with an "impure" vowel sound that glides from an ah-like position to an ee-like position. The number of diphthong sounds differs between different varieties of English, but the clearest examples are the "long i" sound mentioned here, the "oy" sound, and the "ow" sound of cow. I believe the "long i" sound is the only one of these three that is commonly represented by a single letter.