Hi elcid, and welcome to the forums.

 Please help me with the following sentences.

 i ) She certainly drives slow in that old Buick of hers.

  She certainly drives slowly in that old Buick of hers.

Can we use slow and slowly either of them in the present context?

Here's what www.m-w.com says about using "slow" as an adverb (I've added the bold the sentence near the end):  usage Some commentators claim that careful writers avoid the adverb slow, in spite of the fact that it has had over four centuries of usage. In actual practice, slow and slowly are not used in quite the same way. Slow is almost always used with verbs that denote movement or action, and it regularly follows the verb it modifies.  Slowly is used before the verb and with participial adjectives. Slowly is used after verbs where slow might also be used <burn slow or slowly> and after verbs where slow would be unidiomatic

So -- either one..

ii) He spoke sharply, quickly, and to the point.

   He spoke sharp, quick, and to the point.

I would use only sharply and quickly.

What is the meaning of this one?

iii)He did wrong by her.

This is an idiomatic phrasing. He did something that caused her some harm, probably emotional harm.