There is no "best" tolerance. If there was, the code would use it. No such thing.
Best would surely be defined differently for everyone, since someone might just want a quick and very approximate answer, whereas someone else will want the answer correct to within the eyelash of a gnat.
As for making it faster, if it was easily made faster, the person who wrote the code would have done so in the first place. You and every other user of a computer always wants it to run faster. The best way to ensure that is to buy a faster computer.
You need to accept that multidimensional numerical integration of a general function is a computationally intensive thing. Without knowing anything at all about your kernel, it is literally impossible to guess how you might make it faster.
You MIGHT be able to do something, by using the profile tool on your function. Perhaps there are optimizations you might achieve. For me to know what you might do is tough, as my crystal ball is always on the fritz. (Extra points to anyone who knows where the phrase "on the fritz" comes from.)
