1) Some researchers ______ for links between mobile

The OAs are A and C.
So Hussain gets both right. I got both of these wrong. The OEs werent great.
These are slightly tricky. I am not confused between simple past and present perfect. I know what they are in theory but which one to use when is slightly confusing.

Any light on some basics will be helpful.
Kudos to Hussain for a good effort.
Thank you.

Check this great effort by gmat club team
gmat-grammar-book-verbs-96445.html

Also do go through the detailed verbal grammer book here
gmat-grammar-book-96532.html

Best of luck!!

1. A - Have looked is appropriate as stated by Hussain.

2. C- this event is not ongoing. It is completed somewhere in th past. Thus simple past tense is used.

1.A & 2.C

The 1st one was pretty simple keeping the tense in mind.
Second one got me thinking between A & C. C make the sentence look clean and better, so C.

The As are present perfect tenses, Bs are past perfect and Cs are past tense. Past perfect tense is used to show that an event happened in the past prior to another event in the past. Past tense shows that an event happened in the past. Present perfect expresses an event that has present consequences. For example;

The boy saw the car. (Emphasis is on the fact that the boy saw the car.)
The boy has seen the car. (Emphasis is on the present state of the boy, resulting from the fact that he saw the car.)

Also,

Example A: How does John feel about the test? John is nervous about his test, but he has prepared, so I think he'll do fine.

Example B: What did John do last night? Last night, John watched some TV and prepared for the test.

Notice that in example A, we're talking about something happening in the present, but it's necessary to mention something that happened in the past.

In example B, we're telling a story about the past.

So an understanding of the context would signify which tense to use.