To answer your question without seeing your home is difficult at best. If you live in an area of the country where radon is an issue you may need to seal it off to prevent radon from entering into the basement. Even if you do not live in areas where radon is found, I would still have a test done just to be sure. Pro-Lab in Florida has do it yourself test kits that a home owner can use to determine if radon is present. They are not to expensive but can provide a basic screening of this cancer causing gas.
Well you sort of did the job half way. However if you suceeded in stopping any water from entering into the floor you did what you need. However, most walls Not all are the source of the leakage. As they age and foundation settles cracks develop on the walls and water enters into them. If your walls had any signs of moisture such as a white powder that may have developed on them water is present within them.
You simply drill 1/2 inch holes in each block next to the foundation in each cell of the block so any water that may enter within the wall has a way to escape.
As far as construction of any finished wall within the basement. I would suggest that you construct the finished wall so there is a air space behind the wall. Then provide a ventilation system such as
http://www.waveventilation.com...urce=waveventilation There are many other brands of this system out there, but you will get the idea once you see their system and how this method works. We have constructed our own systems with a radon vent fan and de-humidistat controls and saved big dollars from the commercial systems sold such as this. This will allow for any humidity that may enter into the structure to have a way to escape before it does any damage.
Now just to understand, there are many other methods of construction of basement walls out there. Many contractors have success in building right against the walls of the basement. I however think that this is a mistake. Having this space allows for ventilation, wires to run for phone, cable etc that you may have forgot. But for most cases a place in which to provide ventilation so any dampness that does occur can be removed with air flow.