First post on here. Would ideally be a response to @Rand but I don't have enough reputation. Apologies if this is the wrong way to go about it.
Using a lot of the same logic as @Rand, but with different conclusions for some parts.
A Quantity you always see.
Facepalm, and "Oh it's me!"
Not seen in combs, but sometimes in balls,
"Goal! Hi me" from far he calls.
This is very obviously FIVE. Palm points to 5 fingers. Soccer balls are typically constructed by pentagons and hexagons, while honeycombs are hexagonal. So a pentagon is present on a soccer ball but not on a comb. In the last line "Hi me" is spoken from the numbers perspective, so it is probably pointing to the phrase "high five".
If I were an ass, then I'd be a Finnish wire,
I may be small, yet I am entire.
Alpha, one number - eternity for me
The first you learn, the first you see!
Here my guess would be ZERO. This is based mostly on the third line which makes me think of aleph-null (the cardinality of all natural numbers). This also fits well with the mention of eternity/inifinty. Zero is also a small number and arguably the first number as mentioned in the last line.
Upright, or lying, it differs in country.
Nonetheless, I'm still that worthy!
Ben, not ten, sees me the most,
And I'm perfect, that's what I'd boast!
My guess here would be SIX. It is based on the assumption that all the answers are single digits and the last line makes me believe we are looking for a perfect number (numbers that are equal to the sum of its proper divisors). The number 6 is the smallest, and the only single digit, perfect number. Not sure how the rest of the verse fits with that.
Father, Son, and Holy Ghost,
This has been valued to the utmost.
Faith, hope, and love remain,
What value I obtain!
This is most likely THREE like @Rand says. Based on the holy trinity and the triplet of "Faith, hope and love".
Deviously new, and weirdly told,
Yet messily, since me, it's been so so old.
After all, the match you've won,
And with that the guessing's done.
This one I am very unsure about. The only thing I can think of would be SEVEN. This is based on the fact that when asked to guess a number between 1-10 the majority of people will default to 7 for some reason. I'm pretty sure this is wrong though.
Five times four is five in all,
Together we give out all.
The last of all to keep him hidden
Senpais, what a riddle I have written!
I'm not sure how this verse plays into the answer at all.
"Bits and bits" made me think that maybe the answer had something to do with the binary representation of the numbers, but that didn't lead me anywhere. The combination of "bits and bits" and the word "told" makes me believe the answer might be related to leet-speak, so that each number represents the letter it most resembels. With the digits I have given so far (50637) that would give something like SOGET, but that doesn't really tell me anything. So either some of my digits are wrong, or I'm way off with my thinking at the end here.
Not very condifident in the final answer I came up with, but parts of this I'm pretty certain about.