1) Not if you have another squash plant specifically another C. pepo. Another summer squash, a pumpkin or an ornamental gourd (as well as others) can pollinate your female zucchini. The only thing that the cross-pollination affects is your seeds, which you normally don't even want in a summer squash. However, if you know there was no way it got pollinated you can still cut it off and eat it. The only thing that is different is that it is much smaller.

2) Poor pollination

3) Male flowers I wouldn't bother with, but female flowers I would absolutely remove. If you do what I recommended for question one then you wouldn't have old, rotting females.

Female flowers stay open for a couple of days but the males only for a day. I think that's why we get males first. Seems to me that strange shaped fruit is related to pollination....if it looks ok, eat it. I don't groom my plants so I let the blooms die naturally but I would think you could remove them......just remember those yellow blooms are what the bees look for so more yellow probably will get you more bees.

Shebear,
I want to clear something up for you so that you aren't confused. You seem to have a problem with my statement of poor pollination affecting fruit shape. This is probably because I am sure you have also heard that cross-pollination will not affect fruit shape, color, taste or anything like that. It will only affect the seeds in the squash.

Both my statement and the cross pollination statement are accurate. The cross-pollination statement is talking about if you cross something yellow and bumpy with something green and round you won't end up with a fruit on the current years plant that is green and bumpy or yellow and round or anything like that. My statement is concerning maturing seeds. If there isn't enough pollen to fertilize all the seeds the portion of the fruit that wasn't fertilized will grow disproportional to the rest of the fruit because the seed are not enlarging.

Incomplete pollination, which is what I was talking about when I said poor pollination will affect fruit growth rates. In zucchini (and likely others) there are two types of pollen those with fast growing pollen tubes and slow growing pollen tubes. When there is a lot of pollen all the seeds are pollinated by fast growing pollen tubes. When there is a small load of pollen the fast and slow tubes can compete and if there isn't enough of either then the zucchini is pollinated from the stem end to the flower end. I know it seems strange the portion of the zucchini closest to the flower is the last to be pollinated.

This is a good paper on the subject if you are interested:
Effects of Pollen Competition on Progeny Performance in a Heterozygous Cucurbit
Mauricio Quesada; James A. Winsor; Andrew G. Stephenson
The American Naturalist, Vol. 142, No. 4. (Oct., 1993), pp. 694-706.