Some of my privet hedging is a bit sparse around the bottom, which leaves huge unsightly gaps. Is there any way of encouraging it to sprout some new shoots, e.g. making nicks in the main stalk?

I have a great privet hedge that many neighbors comment on.
Make sure that you avoid the tendency to trim the top wider than the base. Your verticle lines should be 90 degrees to the ground. I do my main trimming after the blossoms have mostly disappeared. In the winter, cut out about 1/3 of the oldest main branches at the ground. Fertilize your hedge with a balanced fertilizer. I prefer 12-12-12. Water in times of drought or if your hedge is young.

I wouldn’t do the 1/3 winter trimming thing untill the hedge has been in place 10-15 years.

I have a 6X3 fish pond and I also have a waterfall and 1 fish.

this link should help you figure it out. I think the "balance" of animal and plant life is most beneficial.
Plants suck up the excess nutrients that the algae are drawn to, so in a way just adding plants could help a lot.

I know because of trees we breath but how were they formed and why do they pair so much with our body’s…..Trees are here for a reason to allow us humans to live on this earth how did this all happen?

While it would be easiest to say that some one placed them here for our benefit, that may not be the case.

Life is relative to each other, and many animals form symbiotic relations on their own. Trees are not here for our benefit, nor are plants ‘made’ to be eaten. This can be seen in only 1% of their energy level being passed on to their consumer.

It is true, without the recycling of CO2 into O2, life that breathes O2 on our planet would not have lasted long, however this is just a fortunate side effect. If you really want true perspective of how important trees are, consider the Taiga. A frozen land where animal life does not exist, but plants still stand strong. This single area of our world is large enough, and the trees there produce so much Oxygen that they actually change the entire composition of our atmosphere.

Plant life in an area that won’t support animal life. Plants are merely here to grow and reproduce their genes. Nothing more, Nothing less.

I really dont want to just put random flowers in the front, I want it to look good.

You didn’t mention your light requirements so I can’t help you with species. But as for color, I’d go with pale yellow, sky blue and pastel peach.
Depending on your light requirements, this may include achillea (yarrow), hardy geranium, helianthemum, pulmonaria (lungwort), oenethra, coreopsis and many many others. You may want to include a few annuals with your perennials for summer-long bloom. Try browsing a plant and seed catalogue for ideas.
Always plant in clumps rather than many different individual plants. At home, I like to use what I call "anchor" plants; repeat these plantings at the ends and in the center, and fill in with different varieties. It will give your garden a pulled-together appearance. You may want to "anchor" with some lovely flowering shrubs, like viburnum, itea, hydrangea, spirea and weigela. All come in a varity of colors; again what you plant will depend on your light requirements.

Need a pond plant to put in a pottery fountain. Only thing is the opening is only about 18 inches, so the plant will be right next to the fountain. I need a pond plant that does well in turbulent waters. Will papyrus work? Any other suggestions?

I have a pickerel rush and a horsetail right next to my waterfall. I also have actually grown parrot’s feather right in the waterfall. For potted plants, you’ll need to cover the soil with about an inch of gravel to keep the dirt from washing out. Use a solid pot, not one of those screen types.

Papyrus would probably do OK, as would graceful cattails or one of the cypruses.

In an effort to save money, I plant a lot of my bedding plants from seed instead of buying blooming plants. Does anyone know how long those plants that nurseries sell have been growing? It seems like my seedlings (particularly dianthus, sweet william, and snapdragon) are very straggly that whole first growing season, winter over nicely (we have fairly mild winters), and look great the following spring.

seven or eight weeks at least in ideal light and moisture conditions.