difference between besides, apart from, aside from, in addition to, on the other hand, moreover, furthermore, other than, and except for

besides  - (түүнээс гадна) in addition to someone or something; except for someone or something
furthermore - (жичдээ, цаашилбал) in addition to what has just been stated. Furthermore is used especially to add a point to an argument.
synonym moreoverin addition to / in addition - (үүндээр бас)
on the other hand (нөгөөтүүр, нөгөө талаас) used to introduce different points of view, ideas, etc., especially when they are opposites
moreover  -  (тэрч байтугай, түүгээр үл барам) used to introduce some new information that adds to or supports what you have said previously
synonym in additionapart from - ( үүнээс гадна)
except forI've finished apart from the last question.in addition to; as well as
Apart from their house in Connecticut, they also have a cottage in Nantucket.
aside from - ( үүнээс гадна) apart from
= apart from
except for  - (үүнийг оролцуулахгүй бол) used before you mention the only thing or person about which a statement is not true. 

(except and except for are the same. you can use either of them.
for example: We work every day except Sunday.
                     We work every day except for Sunday.)
other than - (аас ондоо) (usually used in negative sentences) 
1 exceptI don't know any French people other than you. 2 (formal) different or in a different way from; notI have never known him to behave other than selfishly.
otherwise - (өөр маягаар, өөр тохиолдолд, үгүй бол)
1 used to state what the result would be if something did not happen or if the situation were different
        My parents lent me the money. Otherwise, I couldn't have afforded the trip.
2 apart from that
        There was some music playing upstairs. Otherwise the house was silent.
3 in a different way to the way mentioned; differently
        It is not permitted to sell or otherwise distribute copies of past examination papers.
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for example
1.
the city provides many cultural opportunities.
               
                                                       Moreover ,
                                                       Furthermore,  
It has an excellent art museum.   In addition,               it has a fine symphony orchestra.
                                                       Besides,
                                                       Otherwise,
                                                       on the other hand,

2.
the city provides many cultural opportunities.
               
                                                           , moreover ,
                                                           , furthermore,  
It has an excellent art museum. It   , in addition,       has a fine symphony orchestra.
                                                           , besides,
                                                           , otherwise,
                                                           , on the other hand,
3.
the city provides many cultural opportunities.
               
                                                                                                                , moreover .
                                                                                                                , furthermore. 
It has an excellent art museum.   It has a fine symphony orchestra  , in addition.      .
                                                                                                                , besides.
                                                                                                                , otherwise.
                                                                                                                ,  on the other hand.

• He said he had not discussed the matter with her. Furthermore, he had not even contacted her.
• There is,moreover, increasing evidence 
• I don't really want to go. Besides, it's too late now.
• There is, in addition, one further point to make.

• It was a difficult time. Apart from everything else, we had financial problems.
• I've got no family besides my parents.

what is the difference between in addition and in addition to?

There is little difference in meaning, but after "in addition to" you would need a noun of some description.

Examples:

The brothers want to sell tomatoes. In addition, they would like to sell potatoes.

The brothers want to sell tomatoes. In addition to tomatoes, they would like to sell potatoes.

The brothers want to sell tomatoes. In addition to THIS, they would like to sell potatoes.

In addition to tomatoes, the brothers also want to sell potatoes.

What is the difference between a prepositional phrase and an adverb clause?

A prepositional phrase is a phrase which consists of a preposition and a noun and functions as an adjective or an adverb.

I'll do my homework after dinner.
'after dinner' is a prepositional phrase and functions as an adverb.

An adverb clause is a clause which consists of a conjunction,a subject and a predicate and functions as an adverb.

I'll do my homework after I have dinner.
'after I have dinner' is an adverbial clause.

               "Besides" vs. “Aside from"

• Usually, “besides" and “aside from" can be used interchangeably; however, there is a very slight difference. "Besides" is often considered to be a tiny bit less formal than “aside from".

• They are very nearly the same thing. I would say that, unless you’re using “besides" as an adverb or “aside" without the “from", it would be all right to use them interchangeably. If you’re writing something more formal, you might go with “aside from", and even then, there is only a slight difference.

difference between furthermore / moreover

• The difference in these two is so subtle, most people would use these interchangeably, usually with a meaning of "in addition" which would be the less formal way of saying both.
  If you want to get very detailed, to me furthermore introduces an additional concept as a straight fact, whereas moreover suggests that there is a perceived link between the additional information.
  
  More extreme versions of those sentences might read:
  1) The car's acceleration performance is poor and the fuel consumption is extremely high. (The reader is left to draw their own conclusions based on these facts)
  2) The car's acceleration performance is poor and what's more, the fuel consumption is extremely high. (The writer is possibly suggesting that this combination makes for a poor car)
  
  As I said, it's subtle and I would say it's definitely possible to imply the second meaning also with 'furthermore'.

• Most speakers use them synonymously; some speakers don't:
  
  moreover, beyond what has been said
  furthermore, in addition to what has been said
  
  [1] “The acceleration performance of this car model is very poor; furthermore, its fuel consumption is extremely high.” 
  
  [2] “The acceleration performance of this car is very poor; moreover, its fuel consumption is extremely high.” 
  
  In the first example, the speaker gives 'an impartial, co-equal assessment of the two inadequacies of the car model', whereas in the second example, a critical judgmental sense against the fuel consumption aspect is conveyed. The speaker’s bias shows somewhat.