Low water pressure:
If you are on a county fed plumbing system, low water pressure is typically due to a faulty or reduced PRV (or Pressure Reducer Valve). This can be adjusted up or down to accomodate your needs. If it can not be adjusted it is typically due to a faulty diaphragm inside the PRV. A faulty diaphragm can also lead to a vibration noise in your pipes.
Continuously running toilet:
A continuously running toilet is typically due to a bad diaphragm inside the flush valve, or debris has blocked the diaphragm from closing all the way. In some cases the diaphragm can be cleaned or replaced to stop this problem. If not the flush valve will have to be removed or replaced.
A toilet that occasionally runs for a few seconds:
A toilet that occasionally turns on is due to an aged or bad flush valve flapper. If you are running into this problem the best thing to do is replace the flapper, making sure to clean the seat of the flush valve.
Low water pressure at an individual fixture:
There are two main causes for low water pressure at one fixture.
1: Debris has entered the plumbing supply lines and clogged up your aerorater. The areorater can be removed and cleaned allowing proper water flow.
2: One of the supply lines could potentially be kinked causing disruption in the water flow.
One toilet in your house gets stopped up more than the other:
If one toilet in your home works better than the other, you need to first make sure that they are flushing the same volume of water. If one is a newer toilet and one is an older toilet, the older toilet will always work better. The older toilet flushes three gallons as opposed to the 1.6 liter of the new style toilets. If both toilets are 1.6 liters or new style toilets, and one flushes better than the other and they are not the same brand, its simply because one is simply just a better designed toilet.
Stopped up bathroom sink:
When a bathroom sinks gets stopped up, most of the time it is a lot simpler than what you would think. Seven out of ten times the obstruction is within the first five inches. This can very easily be solved by removing your stopper from the linkage and pulling out the obstruction by hand.