Will a pregnancy test be accurate 2 days before expected period ?

Probably not.  There's really no point in taking a drug store urine test that early.  If you really need to know that soon, get a blood test.

The "problem" is that the hormone these tests look for doubles about ever 2-3 days in the first few weeks after conception. Even with the new, more sensitive tests, it is very likely you won't have a high enough concentration of hCG in your urine yet to register on a test strip.  Generally, you'd be wise to either get a blood test (which is more accurate and can fine lower levels of hCG) or to wait until your period is at least 5 days late.  

Yes absolutely. I was 8 days pregnant when my test turned positive. I did buy a Frer though which is first response early result 

You typically have to wait four weeks before taking a pregnancy test but there are somewhere you can find out sooner. By four weeks it wouldn't matter when your period was due because you've already conceived and therefore you're pregnant. False negatives are extremely common and false positives are extremely rare.

Sometimes it is.  If you get a positive result - you can trust that.

If you get a negative result before a period is due - then it MIGHT just be because the hormones aren't strong enough yet.

Maybe or maybe not.  

You should always wait until your period is actually late before you test. Why can't you just wait a few days?