Wouldn't someone notice a member of the Sons of The Harpy running forward to stab Dany?
On the one hand people (or at least the important ones, i.e. Dany's few Unsullied guards) didn't notice the first assassin first and foremost because his attack came pretty suprisingly. He waited in the whole crowd for the right moment, when everyone was captivated by the pit fight and approached her from the back, as Hegemon elaborates in his comment. And the few audience member noticing him might either not have cared, be surprised too, or just not have dared to say anything (i.e. next answer).
Where were they hiding? Do they just stand up from the crowd, put on their masks and start fighting?
Indeed they do. Now first of all you have to consider that the larger population seems to be at best rather indifferent to the deeds of the Sons of the Harpy and if a bunch of people next to you suddently rise and put on those masks, you're not gonna cry out "Hey unknown queen, watch out!". Those people that did care for Daenerys were likely suprised and intimidated by their sudden uprisal.
Add to this, that the masks aren't only for diguise but also for identification among the rebels and as a symbolic gesture. It doesn't really matter so much if your seat neighbour recognizes your face before you put on the mask, he won't run to the courts with that information, especially not when you succeed in killing the queen and reinstantiating the old order and don't have much hesitation to murder any non-Harpy audience members anyway.
Why don't they throw their knifes at Dany? Wasn't she in close range?
Well, granted, that might not have been such a bad idea. But well, they just didn't do it. Other than that wasn't what happened since we don't want a dead Daenerys I don't have a much better answer either.
Do the Sons include former slaves as well? (we see quite a few who are shirtless)
Now on the one hand that may simply have been disguise by the rich people in order to better scatter through all the audience. And on the other hand you also have consider the factor that likely not all the former slaves were entirely on Dany's side, however unusual that may sound. You have to understand that those people grew up as slaves all their lives and in physical as well as psychological dependence on their masters and their status as slaves. Not everyone might be happy about being freed, since apart from the lack of freedom and the possibly harsh treatment as slaves they also had economical security and somewhat kind of a family. So I don't have doubt that some of the less strong-willed former slaves might even support their former masters in reacquiring the status quo.
Also couldn't they have attacked Dany in the lesser pit (shown in S05E07) when she had fewer guards?
In the lesser pit in S05E07 there weren't any people other than Dany and some select few from her staff at all. It was a "private session" that wasn't even in the city of Meereen but somewhere in the outskirts without a whole large crowd to hide under and to fight for the Sons of the Harpy.