1) First, you should know that these statements are using dialect and some informal English. "I ain't got abandonment issues" is an informal way of saying, "I am not afraid or uncomfortable with being left alone." "Truckers on the blacktop, making do" is an incomplete sentence, but it is a truck driver talking about driving on "black top" which is another name for the material a road is made of (asphalt), and "making do" is an expression people use when they don't have all of the materials or options they would like to have but choose to use what they do have.
2) First, you should know that tweets often have typos and mistakes. "He should say that" doesn't make sense within the sentence, so you are right to not understand it. I think that President Trump made a mistake when writing his tweet, but he is trying to say, "Even though Obama thinks he could have won against me in the election, he is too unpopular and has made too many mistakes for that to be true. Obama would have lost against me"
3) You are right that there are expressions like, "I am going out," I will go out there," and "time is running out." It might be common to hear "out" used as you did in your sentence, but a clearer sentence would be, "I only buy medicine that is a year away from expiring." Using the sentence you first wrote could be mistaken as meaning that you buy medicine only if it expired one year ago, which is unlikely to ever be said because that is a bad idea hahaha.
Good questions. Keep up the good work.