關於英文文法的問題?

1. a lot of = lots of ，沒有lot of的用法。應是筆誤。
名詞lot屬於「普通可數名詞」，單數時，前面必須加上不定冠詞a，複數形可不使用冠詞。

2. rather than的前後應用相同詞性的字或詞表示「對應關係」：
I prefer "to take my own lunch to the office" rather than "(to) eat in a restaurant."不定詞。
He is "a writer" rather than "a scholar."名詞
It is "sultry" rather than "warm."形容詞
Rather than "travel by car," I'd prefer "to walk."不定詞

(a) prefer + doing + to + doing
I prefer "standing" to "sitting."動名詞相對應
(b) prefer + to do + rather than + (to) do
I prefer "to wait" rather than "(to) go at once."不定詞相對應（後面不定詞的記號to省略，以免重複）
prefer後面如使用rather than時，不使用介系詞to；prefer A to B; prefer A rather than B均是表示要前者，不要後者。

I prefer "taking my lunch to the office" to "eating in a restaurant."
是prefer A to B的關係，A／B都是「動名詞」，其中的to是介系詞。

(1) a lot; also informal "lots", adv. is used with adjective and adverb to mean "much":-eg:-Her new hairstyle has made lots of difference(=much) difference...Its a printing error.
(2) By figure of speech,style of writing, In grammar, gerund is a noun in the form of the present participle of a verb (that is ,ending in --ing)eg:-"eating" in rather than "eating" in restaurant.
By the figure of speech, style of writing in grammar, participle is a noun in grammar for a word formed from a verb, ending in --ing to mean the present participle, Or --ed, --en, etc to mean the past participle;(while participial is an adjective)eg:- "eating" in rather than "eating" in restaurant.
Hence in (2) it is a matter of style of writing in grammar relating to verb=a verbal noun=gerund Or participle.