Using a one-character vs two-character word
Tl;dr: You may think of 年 as bearing the concept of 'year', and 父 bearing the concept of 'father' (in the usually bisyllabic modern Chinese).

Put simply, modern Chinese uses bisyllabic words (雙音節詞) pervasively. Monosyllabic words (單音節詞) are much rarer. It is precisely for this reason that we only parse individual characters in classical Chinese (and also idioms in modern Chinese!), but not modern Chinese in general:

Modern Chinese: 妻子 ‘wife’
Classical Chinese: 妻 子 ‘wife and son’


In modern Chinese, we use a plethora of bisyllabic words to express different nuances:

請填寫您的出生年分。 Please write your year of birth.
《追憶逝水年華》 In Search of Lost Time 

年分 is neutral; it also refers to a particular year. But 年華 is much more literary and refers to many years, or more accurately speaking, the passing of time.

父親節快樂！ Happy Fathers' Day!
為子慶生慈父扮鹹蛋超人 Loving father pretends to be Ultraman to celebrate son's birthday
Adele生父Mark Evans傳癌症病逝 Adele's biological father Mark Evans rumoured to have died of cancer

父親 is again a neutral saying; 慈父 meanwhile is very approving of the father. 生父, like English, emphasises on the biological relationship between the father and the offspring.

That does not mean we do not use monosyllabic words in modern Chinese. 年 can be a counter in

一年 one year
那些年 those (bygone) years,

and 父 alone is perfectly understood and may be used in newspaper headlines out of concision:

子稱被父奪走公司 Son claims company usurped by father

We do not say it like this in speech or normal writing.