Is there any dictionary that shows the decomposition of each word into these three parts, if application at all? For instance, "incapable" is divided into prefix "in", root "cap", and suffix "able". Thanks in advance.
Most of them if they give an etymology.
Taking your examples, the OED gives:
medieval Latin incapābilis, < in- (in- prefix3) + capābilis capable adj. and n. (French incapable is known from 1517 (Hatzfeld & Darmesteter); capable in English from c1560.)
The looking up capable
French capable (= Provençal capable), < late Latin capābil-em (in early theological use: see Du Cange), irregularly < Latin capĕre to take. The regular formation would have been capibilis; perhaps capābilis was influenced by capax: Beda Lib. de Orthogr. has ‘capax, qui facile capit; capabilis, qui facile capitur’ (Du Cange); so Augustine, but Cassiodorus c575 has it in the active sense = capax, as in the modern languages.
Middle French, from in- + capable capable
Then looking up capable
Middle French or Late Latin; Middle French capable, from Late Latin capabilis, irregular from Latin capere to take.
So we can see, in‑ + (capere + ‑bilis) with ‑bilis / -abilis being the source of the ‑ble / ‑able suffixes.
Now, this does not break things down quite as neatly as in‑ + cap + ‑able, or even in‑ capere + ‑able but that's because the English word incapable is not in‑ + cap + ‑able.
Latin capabilis means comprehensible or intelligent, or being able to be received (in Christian theological use, God and specifically the Holy Spirit is described as capabilis).
This is not what the English word capable means, and nor did capere come into English with it. Hence not only is there no capere root (you suggest cap, but on what evidence?) in English, (the closest in English would be have and heave), but the English word capable does not mean the same thing as its source.
So while the dictionaries don't give as neat a breakdown as you ask for, that's because the reality they are describing does not have such a neat breakdown, and giving it would be an error.