Were some parts of the law abolished or "not one jot will by any means pass from the law"? Were some parts of the law cancelled or the whole law in its completeness should continue untill the heaven and the earth disappear? 

Some parts of the New Testament clearly state that some portions of the law have been abolished with the death, resurrection and ascension of Christ (see examples in the end of this question). How does it go along with the following words of the Savior:


  I tell you the truth, until heaven and earth disappear, not the
  smallest letter, not the least stroke of a pen, will by any means
  disappear from the Law until everything is accomplished (Matthew 5:18 AKJV)




Examples of some portions of the law that are pronounced as cancelled in the New Testament: 


Circumcision:


  For in Christ Jesus neither circumcision avails any thing, nor
  uncircumcision, but a new creature (Gal. 6:15 AKJV)

Sacrifices:


  7:11"If therefore perfection were by the Levitical priesthood, (for under
  it the people received the law,) what further need [was there then]
  that another priest should rise after the order of Melchisedec, and
  not be called after the order of Aaron?
  
  ...
  
  15[yet] there arises another
  Priest,
  
  16who is made not after the law of a carnal commandment, but
  after the power of an endless life
  
  ...
  
  18For there is verily a
  disannulling of the commandment going before for its weakness and
  unprofitableness. 
  
  19For the law made nothing perfect, but the bringing
  in of a better hope [did]; by which we draw nigh unto God
  
  ...
  
  28For the
  law makes men high priests which have infirmity; but the word of the
  oath, which was since the law, [makes] the Son, who is consecrated for
  ever
  
  ...
  
  8:6[He] has obtained a more excellent ministry, by how much also
  He is the mediator of a better covenant, which was established upon
  better promises. 
  
  7For if that first [covenant] had been faultless, then
  should no place have been sought for the second. 
  
  8For finding fault
  with them, he saith, Behold, the days come, saith the Lord, when I
  will make a new covenant with the house of Israel and with the house
  of Judah
  
  ...
  
  13In that he saith, A new [covenant], he hath made the first
  old. Now that which decays and waxes old [is] ready to vanish away
  
  ...
  
  10:1For the law having a shadow of good things to come, [and] not the very
  image of the things, can never with those sacrifices which they
  offered year by year continually make the comers thereunto perfect.
  
  2For then would they not have ceased to be offered? because that the
  worshipers once purged should have had no more conscience of sins. 
  
  3But
  in those [sacrifices there is] a remembrance again [made] of sins
  every year. 
  
  4For [it is] not possible that the blood of bulls and of
  goats should take away sins
  
  ...
  
  14by one offering He has perfected
  for ever them that are sanctified"  (Heb. 7:11, 15-16, 18-19, 28,
  8:6-8, 13, 10:1-4, 14 AKJV)
Many Christians agree that there are three distinct kinds of laws in the old testament, and that one of them is eternal.


The moral law that declares how man should live.  
The civil law that was the legal structures for the ancient nation of Israel.
The ceremonial law that declared how ancient Israel was to worship.


The moral law is believed to be eternal.  While it's not perfectly clear what's in the moral law and what is in the other two categories the Ten Commandments as well as passages like Deuteronomy 6:5 are in the moral law.

Both the examples in your question would fall into the ceremonial law.  Many Christians believe that the ceremonial law was either abolished at the death of Christ or completely fulfilled at the death of Christ.  Obviously Christ was and is the eternal sacrifice.  The specific sacrifices of the Old Testament are no longer needed.  As for circumcision it too is fulfilled in a different way.


  Philippians 3:3 (ESV)  
   
   3For we are the circumcision, who worship by the Spirit of God and glory in Christ Jesus and put no confidence in the flesh—  
    


As for the civil law which would include the punishments specified for crimes and the like, it obviously ended when ancient Israel as a nation-state ended.

That said, while some of the laws in the Old Testament don't hold direct sway over our lives any more, remember:


  2 Timothy 3:16-17 (ESV)  
   
   16 All Scripture is breathed out by God and profitable for teaching, for reproof, for correction, and for training in righteousness, 17that the man of God may be competent, equipped for every good work.