No you don't need a tank to simply pump water from a lake. You would only need a tank if your using a pressure switch to turn the pump on and off.
You just need to adjust the pressure switch on the pump to your desired pressure...typically around 50 psi. Sometimes the springs in the pressure switch get old, and just need tightening.
you would need a tool which is called a pressure tester, if you see a leak from the water pump during the test then your water pump is bad and need to be replaced a.s.a.p
So that you will have water pressure from gravity.
There is normally not a pump on a water heater. The water is moved through normal water pressure. If you are having problems with getting hot water through, it may be that the pipes are corroding or pinched, slowing the flow. Or the hot water heater itself is leaking.
There are many different ways to use a 'water pressure pump' . Any water pump will build up pressure, this is the basic principle of well pumps, and similar. Most are 'used' by a pressure switch which turns the pump on when pressure decreases to a certain point.
a 2 to 5 gpm [gal per minuit ] pump, you don,t have city water ? if your on a standard water supply, you don,t need a extra pump, if your on a well then I have a deep well pump in mine that gives me 70 lbs of pressure,
The inlet pressure can be as low as 45 PSI as long as there is a flow of about 3 gpm. The pump will easily pump it to 1500 psi through the appropriate nozzle
If you mean a well tank, the water is forced in by the pump. The residual air pressure pushes the water out to the faucets.
It provides it's own pressure. It has it's own pump which is used to create the needed pressure to wash the dishes.
The pressure switch is usually on the pump if it's a jet pump, or at the base of the pressure tank if a submersible pump.
If you seem to have unusually low pressure or if your pump is running a lot then you need the system checked by a professional. Not necessarily a plumber.
Normally pressure tanks come with about 30 p.s.i. pressure in them,but depending on the type of water system you may need to adjust the pressure. You always want the pressure of the empty tank to be less than the turn on pressure of your pressure switch on your pump(if you have a pump) about 5 p.s.i. less should do it.