How long can sperm live on environmental surfaces?

They die as they dry out, so it depends on how quickly they dry. They also are killed by fresh(tap) water due to osmotic shock(they "explode"). Soap and detergents such as those used for laundering and hand washing also kill them, as these substances strip off the cell membrane("skin") of the sperm. These methods kill sperm very quickly.

Please note, while sperm are relatively easy to kill on environmental surfaces, do not try to use water or detergents to kill them in the vagina or female reproductive tract. The female tract and the jelly-like consistency of human semen protect them from mixing well with water once inside the female body. In addition, water and detergent can be harmful to the tissues. This is not a good birth control strategy!

Yes, there is a possibility of getting pregnant even if the penis does not go completely into the vagina. And this is true even if no ejaculation occurred (in other words even if he didn't come/orgasm). Precum can contain sperm and since it only takes one sperm to fertilize an egg- that is technically all you need. Obviously, the chances of getting pregnant this way are much less than if full penetration with ejaculation occurred. This is because even though only one sperm cell is required to fertilize an egg it technically takes an "Army" of sperm to successfully get that one cell to the egg. More information

Precum contains enough sperm to get pregnant. While it may not have millions of sperm like the ejaculate, it is technically enough for a woman to get pregnant.  This is why the withdrawal method of birth control, which is the withdrawal of the penis prior to ejaculation (also known as the "pull and pray" method), is not very effective. It is also why not using a condom at first is not effective.  If your desire is to NOT get pregnant, use a different form of birth control or use a condom the entire time.

I was in a jacuzzi/shower/bathtub/pool and I ejaculated, can my girlfriend get pregnant?

Not unless you ejaculated in her vagina without a condom.

I have had a lot of X-rays/CT scans/radiation therapy in my pelvis area, will my children have problems?

From beginning to end, a sperm cell takes around 64 days to be made by a normal human male. Radiation affects new sperm cells more than older ones. So, a man 2 months after any radiation exposure should have normal sperm again. That being said, there are no guarrantees that sperm after 2 months will be fine, or even that sperm less than 2 months will be affected. A few X-rays shouldn't have enough radiation to cause problems. Ask your doctor if you're thinking about having children while on radiation imaging or therapy.

What is the size of a sperm cell relative to the size of a human ovum (egg)?

A human sperm is about 55 micrometers (µm) in overall length (head-5 µm plus 50 µm flagellum). A mature ovum is between 120-150 µm in diameter. So the ratio would be 1:2 or 1:3 if you were comparing length of the sperm to the diameter of the egg. If you compare the width of a sperm cell ( ~3 µm) to an egg's diameter the ratio would be between 1:40 -1:50.

I have heard that male sperm swim faster and female sperm live longer, is this true?

There is some truth to this idea. There is a technique called "swim up" to help people have some control over the sex of their child, but it is not very effective (ratio from 50/50 to around 60/40 for males/females). It works like this: A sample of sperm cells is spun at a very high speed, which makes all the cells clump together at the bottom of the container. After the spinning is stopped, the sperm cells are allowed to swim freely again. The faster cells (the male sperm cells) swim up out of the clump faster than the female cells(generally) and are collected for use.

Another technique people try is timing sex with ovulation to influence the sex of their child. The arguement is that having sex soon after the woman has ovulated will increase the likelyhood that the faster male sperm will get to the egg first. Whereas sex slightly before ovulation male sperm will die off leaving only the female sperm around to fertilize the egg by the time it is ovulated. Once again, this technique isn't very effective.

How long can sperm live in the female reproductive tract?

Sperm are seldom able to fertilize an egg after 48 hours of storage in a woman. Sperm can be detected 5 days after sex, but there are generally not enough of them or they don't swim very well, so their ability to fertilize an egg is lost. It's still possible, because you only need one cell to fertilize an egg.