Toilets, Sinks, Showers, Tubs and Disposals - Adding a 2nd washroom

We'd want to add a main floor 2 piece washroom.
The room we'll be using is located on the opposite side of the house of the existing second floor washroom.
It should'nt be a problem tying it into the existing drain pipe because the pipe runs along a wall almost directly below this room in the cellar.
My only concern is, should this new washroom drain be vented seperately or will it be sufficiently vented when tied into the main drain?

#2
The main washroom toilet (installed by a previous owner) has a very weak flush where the water swirls and swirls before finally emptying. How does one get a toilet to flush with real power?

Regards

As usual, local codes prevail. Each fixture in the new room will have be vented. Normally this is achieved by running a line off the fixtures drainline and jumping upwards and tying back into the main ventline. If you don't have a vent to tie into, you will PROBABLY have to install one. Check with the code office to see what you have to do.
Toilet problem may be a bowl that is not coated in the trap. Some companies make "value toilets" and save money that way. It makes a rough surface and solids hang up on the roughness. Another problem could be that the holes under the rim are plugged with mineral deposits. These can be inspected with a handheld mirror. They can be cleaned out with a bent metal coat hanger. If this doesn't work, you can turn off the supply to the toilet, flush and then pour in a calcium remover (CLR etc) through the flapper opening and let it sit a while. Then turn water back on and flush. Otherwise, there may be a blockage in the drainline. Good luck.