Sentence Correction

The confusion is with introductory prepositional phrases. Are they always act as a adverbial phrase or ,sometimes ,as adjectival phrases also?

hv a look on following egs.

1. after lunch, they swam for two hours in the pool.

here : after lunch is prepositional adverbial phrase modifying the action in the main clause.

2. They swam for two hours in the pool after lunch.

here it seems to be correct also.

3. They swam for two hours in the pool ,after lunch. A comma before the prepositional phrase.

Is it a correct sentence....or is this sentence is as same as the first sentence.????


see another eg:

Opposition leader Viktor Yanukovych has clearly won, by a 3.48 percentage margin, Ukraine's presidential election held recently.

here:prepositional phrase is set off by pair of commas .....why this is so?....beause is it non essential phrase or something else?

Also, what role does this prepositional phrase play --- adjectival or adverbial? I suppose that it plays an adverbial role as it answers the question "HOW"...

Now lets see this eg....

By a 3.48 percentage margin,Opposition leader Viktor Yanukovych has clearly won Ukraine's presidential election held recently.

here also does this prepositional phrase play the same role/???.....i think that it plays the same role..as it plays in the first sentence..

Introductory prepositional phrases always set up the ground for the action in the main clause...aint it??

So it always plays an adverbial role...aint it??

See another eg:

Like reta, sita enjoys playing cricket.
But here : introductory preposional phrase, like reta, modifies the noun...., sita

hence it is adjectivial phrase rather than a adverbial..aint it??

this , again , can be written as.....
Sita , like reta, enjoys playing cricket. Here " like reta: is non essential phrase ...aint it??


See another eg;;

Of all the countries contiguous to china, USSR has strongly defended borders.(Correct sentence)

here the introductory prepositional phrase is adjectival or adverbial phrase???

USSR , of all the countries contiguous to China, has strongly defended borders. Is the sentence correct??



Confusion #2
some times prepositional phrase come after the comma in the main clause...

For eg: Eco efficiency has become a goal for companies worldwide, with many realizing significant cost savings from such innovations.

Why the prepositional phrase starts with a comma and what role does it play?