* perfective is used in such requests when you wish a certain result
** However, "можно помочь" sounds either detached or "can it be helped", in a pessimistic way (what you are likely to ask your doctor if a serious disease is ever to be found in an examination)
*** So it is "можете мне помочь" ~ "can you help me/ give me a hand"
Now, about perfective/imperfective forms in imperatives. There are certain set constructions in a language. When a person is instructed to take an activity rather than do something specific, it is imperfect. "Говори" is a standard form when an "interrogator" tries to make someone speak. "Скажи" is only used for asking something very specific. Often just as a polite question ("Скажите, вы не знаете, где находится Молодёжная улица?")
The first sentence roughly translates to "And Teshumai Tawindrow immediately ran up to Taffy and started kissing her, hugging and fondling her."
1)
"тут" here implies "and then, this very moment, immediately after"
2)
"и давай" + infinitive is a literary expression meaning that someone starts an activity enthusiastically, maybe even overdoing it
.