Not wanting to rehash all that has been said but it should be noted that the passage about mans days being 120 years does not strictly mean that is the limit God puts on a man's life. If it were such a limit it would likely only be applicable to the wicked with whom God was striving. It has already been noted that it is believe that the building of the ark took about 100 years. I'm not sure any verse gives the exact number of years but people infer it from the text. It may be more probable to take an alternate view of the passage. It is a few verses later that God tells us about Noah and calling him to build the ark and hence seems probable that God was stating how many years God was giving wicked man before he brought the flood upon the earth. 2 Peter 2:5 says that Noah was "...a preacher of righteousness..." It seems from a coupling of the verse about 120 years and this one about Noah preaching righteousness that God also commissioned Noah to warn the wicked of the coming judgment and their need for repentance. In this interpretation the mercy of God was that even in the face of such wickedness he still gave them 120 years of warning and chances to repent before he destroyed them in the flood.
As for the book of Jasher, as it has been previously noted by Nazarite, we should be skeptical of any extra-biblical texts. Just because a book of Jasher is mentioned in scripture doesn't mean the book currently purported to be the book of Jasher is the real deal. There could have been many Jashers who wrote a book. Satan could have inspired anyone to write a book and call it that for the purpose of deceiving people who would later find it and think it was the very book referred to by scripture. Even if it is authentically the book referred to in scripture that does not make it reliable any more than me quoting a history or science book means I agree with everything in it. If God wanted it to be part of scripture then he would have preserved it perfect and ensured that he was among the books that made it into the Holy Bible. That is God's promise in various passages such as Psalms 12:6-7 "The words of the LORD are pure words: as silver tried in a furnace of earth, purified seven times. Thou shalt keep them, O LORD, thou shalt preserve them from this generation for ever." I personally have read a few of the writings purported to be the writings of some of Jesus' apostles and found some of them to be sickeningly blasphemous. Such stories as when Jesus was a child he struck another child dead for bumping into him while running past him is just one example of a story supposedly written by one of Jesus apostles. I will not even mention the name of that apostle lest some here search out the book and read such blasphemy for themselves. As Paul said in Romans 16:19, "...I would have you wise unto that which is good, and simple concerning evil." It's not necessary to read every book, hear every opinion or learn from every teacher. Ecclesiastes 12:12-14, "And further, by these, my son, be admonished: of making many books there is no end; and much study is a weariness of the flesh. Let us hear the conclusion of the whole matter: Fear God, and keep his commandments: for this is the whole duty of man. For God shall bring every work into judgment, with every secret thing, whether it be good, or whether it be evil." 2 Peter 1:3, "According as his divine power hath given unto us all things that pertain unto life and godliness, through the knowledge of him that hath called us to glory and virtue"
As for the question about birds, as other posters have mentioned, there are verses in the Bible about birds. However, without knowing why your friend believes the Bible places a special importance on birds it would be nearly impossible to know how to respond. I think the one poster who mentioned the verse about a sparrow not being able to fall without God knowing was likely on the right track. A lost person is not likely to be familiar with the passages about sacrificing certain birds but probably has heard the verse about the sparrow and maybe Isaiah 40:31 about rising up with wings as eagles. As the other post mentioned, the first is speaking of God's full knowledge of his creation, care therefore, and his comparatively greater love for us than a sparrow. The second passage speaks of the way an eagle soars and would make an interesting discussion on its own. Still a comparison and not a glorification of birds over other creatures. I encourage anyone who is interested to study how an eagle soars. How its is set high and safe from danger, how it can fly so high that is is above the storm clouds remaining safe and dry, how they have been seen by commercial airline pilots they fly so high, how they don't have the strength to soar to such heights on their own but rise on warm air currents called thermals. The comparisons to how God can make us dwell safely from danger, to soar high above all the storms of life, and to do so trusting in a strength that is not our own.
Hope this helps shed a little more light on the situation. May this find you all blessed in all that God has put your hands to.