Before I start, I’d like to say that, in my opinion, that a concise sentence is very subjective. I have also said (in other posts) that a GOOD sentence should be concise as well as clear. With this in mind, I’ll continue.
[b]
- They have monitored the activities of conservationists in a cautious manner.[/b]
They have monitored the activities of conservationists cautiously.
The above is fine.
2. As a matter of fact, a student is less likely to fail an examination if he knows exactly and specifically what topics will be tested.
A student is less likely to fail an examination if he knows exactly which topics will be tested.
‘EXACTLY’ may be omitted.
‘WHICH’ is the correct determiner to use here because there is a finite set of topics which might be tested.
3. There are several important and significant reasons for this decision.
There are several significant reasons for this decision.
You may omit ‘SEVERAL SIGNIFICANT’.
4. The man, who was elected, was not the best.
The elected man was not the best.
In place of ‘the elected man’, we may use ‘the candidate’ or ‘the electee’. I would prefer to use ‘the electee’ for the sake of stopping ambiguity.
5. These apples are fit to be eaten.
These apples are fit.
Can you explain to me,
If we see infinitive in a sentence and then a verb, in the concise version of the sentence we omit/remove this infinitive?
If you eliminate the infinitive, in this case, you are leaving the sentence open to many different interpretations. I.e., if you were to have ‘these apples are fit to eat’ this can mean either ‘these apples may be eaten’ or ‘these apples are able to eat’. A possible solution for this might be…:
These apples may be eaten.
or
One may eat these apples. (this is QUITE formal!)
6. It was the parents who expressed their concern about the old house.
The parents expressed their concern about the old house.
‘THEIR’ may be omitted because it is implied by the verb and subject that the concern is theirs.
‘OLD’ may be omitted because it has no intrinsic value, with regards to the actual meaning of the sentence.
7. It goes without saying that what happened will affect the man’s performance.
What happened will affect the man’s performance.
In this case, the gender of the performer isn’t essential to the sentence (you may omit “man’s”).
8. He returned all what he took.
‘To return’ means ‘to give something back’. As such, we don’t need to know that he’s taken it, as it’s implied by the verb.
‘He returned everything’ is satisfactory.
9. As a matter of fact, they joined and connected the wires.
Though I am not really sure about this I gave this answer to it:
They joined and connected the wires.
Or/
They joined the wires.
I have a feeling that there is a difference between (joined) and (connected)
- join probably means to join the wires together.
- connect means to connect them to the plug or something.
Unless there is some context which does explicitly differentiate the two verbs, we should consider them the same…:
They joined/connected the wires.
10. The basic fundamentals of how to dance were first learned by Jane.
Jane learnt the fundamentals of dancing.
The original sentence suffers from ambiguity - I apologise if I’ve misunderstood the meaning behind it.
11. At that point in time when Martin was a teenager, I was sixty.
When Martin was a teenager, I was sixty.
This seems fine to me.
12. It was Jane who was selected for the final competition.
Jane was selected for the final competition.
We don’t need to mention that it’s the FINAL competition.
13. To cut a long story short, the sea remained calm.
The sea remained calm.
That’s absolutely fine. ‘To cut a long story short,’ is an idiom meaning ‘basically’.
And that’s it!
I hope this has helped you… I’ll endeavour to solve your run-on sentences post tomorrow. Now, I’m half brain-dead from working on this post for half an hour. Enjoy! 
Code.
