In 你多吃点 and 多给他点时间吧, is 多 an adjective or an adverb?
"多" here functions just like "more" in English. It can be an adjective or adverb


  In "多吃点",  '多' (more) is an adverb for the verb '吃'(verb). In English, "多吃点水果"  means "eat fruit more"


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  In "吃多点" , '多点' is an adjective for an omitted object. In English, "吃多点水果" means "eat more fruit"


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  In "多给他点时间吧", '多' (more) is an adverb for the verb '给' (give). In English, "多给他点时间吧" means "give him time more"


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  In "给他多点时间吧", '多点' (more) is an adjective for the noun '时间' (time). In English, "给他多点时间吧" means "give him more time"



多; 很多/ 多点; 多些 preceding a noun is an adjective. e.g. 多糖 (a lot of sugar), 很多糖 (a lot of sugar), 多点糖 (more sugar), 多些糖 (more sugar)
多 preceding a verb is an adverb. e.g. 多加糖 (add sugar more)
[verb + 多了] = [verb + often enough/ too much] ; '多了' is an adverb for the verb.  e.g. "看多了書" (read books often enough) ; "加多了糖" (added too much sugar)



  how about 少，for example in “少吃点” is 少 an adverb here? My dictionary says 少 is only a verb and an adjective. 


少吃 = [少(adv) + 吃(v)]

少点吃 / 少吃点 = [少点(adv) + 吃 (v)]

Actually people say 多点吃 and 少点吃 more often than 多吃点 and 少吃点

Example:

少吃水果 = not often eat fruit (少 is adverb for 吃)

少点吃水果 = eat fruit less; 少吃点水果 = eat fruit less (少点 is adverb for 吃)

吃少点水果 = eat less fruit (少点 is adjective for 水果)