Well, taking sick days that early into a job certainly looks bad, and I'd probably have handed you your walking papers too. While you MAY have had a legitimate reason, it just doesn't look good, and could set the tone for your employment. No one wants to hire someone who is going to be constantly calling in sick. The employer has no way to know if this was an isolated incident, or a fortelling of things to come, and there are too many people looking for work to take a chance on you.
As for the rest of this thread, it depends on what industry you work in, but MOST industries REQUIRE you to be on time at whatever time the boss decides your shift is going to be. Show up late very many times, and you're gone...When you're late, someone else has to cover your absence. Granted, many tech jobs, this doesn't apply, but regardless whether you work late or not, you gotta be there on time, get back from lunch on time, and do your work...Doesn't matter if you can do 8 hrs work in 6 hours or not. If that's the case, you should be the most productive in your "crew", and get 33% more work done than the others...or do you believe that you are required to only do X amount of work and you're done for the day?
I'm a hard-a$$ as a foreman. I insist everyone busts their butts the entire shift. I never ask more than I'm willing to do myself, and on the days when we're slack, I'll join in with them playing cards, drinking coffee, etc., but when we have work to do, LET'S GO!! Wanna chat with someone? GET THEIR PHONE NUMBER AND CALL THEM AT HOME! I don't care how your kid's football/soccer/baseball dance team did, I don't care how the niners/raiders/ Giants, or even the Steelers did on Sunday...We can talk about that sh*t at break or lunch.