Tried to figure out what you mean:
他應我的請求而來
Ta1 ying2 wo3 de0 qing3 qiu2 er2 lai2 (He came at my request.)
...對面而坐...
...dui4 mian4 er2 zuo4...(sitting opposite each other)
...不告而去...
...bu2 gao4 er2 qu4...(French leave)
...一帶而過...
...yi2 dai4 er2 guo4... (skimming)
...掩鼻而過...
...yan3 bi2 er2 guo4...(hold one's nose and leave)
而 gives us a sense of 韻律, without it, these sentences would become a little blunt, though still possible to be understood.
又如 孔氏 論語 學而 子曰 學而時習之 不亦說乎 有朋自遠方來 不亦樂乎 人不知 而不慍 不亦君子乎 「學而時習之」中 「而」字當作繫聯之意 可有遞進之感 然「人不知 而不慍」中 「而」當講反襯 對立之意
Translation:
So let's look at another example, from a famous text 論語 written by students of 孔氏 aka Confucius (551–479 BC), which goes like this: 子曰 學而時習之 不亦說乎 有朋自遠方來 不亦樂乎 人不知 而不慍 不亦君子乎. The first 而, in '學而時習之' (xue2 er2 shi2 xi2 zhi1, which means 'learn something and, in the meanwhile, you go over once in a while') shows us 而 with a sense of 'connection', though a little increase here, because you learn it, good, and going over it, em, even nicer.
In the second instance, in '人不知 而不慍' (ren2 bu4 zhi1 er2 bu2 yun4, which means that 'others people offend you because that they did not know you well, but you keep it very gentle, didn't get mad about them') so here '而' gives a sense of U-turn.
Through the eyes from some Japanese, hope it'll help foreigners understand 而 better. Here I translate the parts that are related to our question:
[接] = conjuction
(Original Japanese Explanation) 並列関係を表わす = (My English Translation) Gives a plain list
(Example) 真實而感人
(Pinyin) zhēn shí ér gǎn rén
(Pinyin, another version) zhen1 shi2 er2 gan3 ren2
(注音)ㄓㄣ ㄕˊ ㄦˊ ㄍㄢˇ ㄖㄣˊ
(Original Japanese Translation) 真実にして感動的 = (My English Translation) Real. Touching.
Note: 真實, real, adjective. 感人, moving, touching, adjective.
相反する関係を表わす = Juxtapose two things with opposite meaning
艷而不俗
yàn ér bù sú
yan4 er2 bu4 su2
ㄧㄢˋ ㄦˊ ㄅㄨˋ ㄙㄨˊ
派手だが俗っぽくない = Gorgeous, but not in a mundane manner
Note: If you remove 而, 艷不俗 is rare, though maybe possible, not as common as 艷而不俗. 艷, gorgeous, adjective. 俗, mundane, adjective. 不 gives negative to the adjective following.
さらに一歩進めた関係を表わす = Shows further step
取而代之
qǔ ér dài zhī
qu3 er3 dai4 zhi1
ㄑㄩˇ ㄦˇ ㄉㄞˋ ㄓ
とって代わる = Replace it
Note: If you remove 而, it gives 取代之, still meaningful though not as common as 取而代之. 取, pick, verb. 代, replace, verb. 之, it, pronoun.
原因・目的を示す語句を動詞につなぐ
為勝利而奮鬥
wèi shèng lì ér fèn dòu
wei4 sheng4 li4 er2 fen4 dou4
ㄨㄟˋ ㄕㄥˋ ㄌㄧˋ ㄦˊ ㄈㄣˋ ㄉㄡˋ
勝利のために奮闘する = Fight for victory
Note: 為, for, preposition. 勝利, victory, noun. 奮鬥, hard working, noun.
仮定を表わす = Gives an "if…"
理論而不與實踐相結合...
lǐ lùn ér bù yǔ shí jiàn xiāng jié hé
li3 lun4 er3 bu4 yu3 shi2 jian4 xiang1 jie2 he2
ㄌㄧˇ ㄌㄨㄣˋ ㄦˊ ㄅㄨˋ ㄩˇ ㄕˊ ㄐㄧㄢˋ ㄒㄧㄤ ㄐㄧㄝˊ ㄏㄜˊ
理論がもし実践と結びつかないなら… = Work on theory without practical proof
Note: 理論, theory, noun, here is a verb, that is, to work out a theory. 與, and. 實踐, practice. 相, with. 結合, combine, verb.