Hi Alex.
I will start with a translation that is as one-to-one as possible with some clarification that is not part of the original line (in square bracktes):
"...and a حَرْف is recognized by [the fact that] it takes/accepts neither the attributes of a اسم nor those of a فعل, such as [the حرف] بلى."
Now the dissection:
"I'm interested in the part "دليلا كبلى" - firstly, I don't understand the meaning behind it - what is it supposed to mean, what semantic function does it have?"
The ك in كبلى simply means "such as". So كبلى means "such as بلى".
"Secondly, I don't comprehend why the word "دليلا" is written in the "النصب" case"
The word دَليلٌ in this context means "sign", "attribute", "feature" etc. In the line it's مفعول به of the verb يقبل ("takes/accepts") , that's why it's in the نصب case; دَلِيلًا.
"is it correct to write two حرفان together as shown in the example: "كبلى"?"
Yes, no problem if the situation calls for it. ك means "such as" and can be attached to anything. Another example is the بِ which has, among others, the meaning of "by ...", "through ..", "by using ..", "by means of ..." etc. We can say بِعَلى ("by على") or بِعَنْ ("by عن"). And so on.