h1 gap?

I have one concern about my H1 visa. My situation is as follows: H1 receive date is May 31, valid date is from July 11. I terminated my previous employment on June 8. I started to work from June 18. (of course, I got paid from this day) . My questions are:


1) Does this mean that there is a 33-day gap on my status?


2) Is it illegal to stay here for these 33 days? I know that it should be fine for a period of time. But I don’t know how long(maybe one month?).


3) I was told even it is legal to stay in the US for a period of time; it is illegal to get paid if I don’t have a valid status. Am I right? But my situation is I got paid from June 18. Any problem for this?


Thanks for your help.