A toilet with 2 problems

I have a toilet that has been chronically leaking water from the tank to the bowl. I replaced the flapper because that seemed to be the most common problem and it looked pretty old. (I don't have any plumbing experience, so I've been going off of others' advice.) I installed the flapper and hooked the chain onto the flushing lever - it has a tiny bit of slack. Now the toilet leaks more than ever - it will either a) run continually; or b) run for a few seconds every couple of minutes. What is the next step I should take to fix this problem? Is there something I have overlooked or a common problem in installing the flapper? It is a standard flapper (with the hooks on either side of the overflow pipe) and a "Standard" toilet.

In reading some posts here and elsewhere, I think there is a second, more serious problem. The toilet often smells of - I think - sewer gas. It does so intermittently, and I have not recognized a pattern. Sometimes the water level in the bowl has seemed low, and I read that this can be a cause, but I'm not sure if that's what's going on here. The toilet is stable and does not rock on the wax seal. What can I do about this problem? Anything besides calling a pro? Also, since this may have been a problem since we bought the house (2 years ago) are there long-term health issues that I should be concerned about?

Thanks for your help!

First, I'm not a pro...

There are some gaskets around the bolts that hold the tank to the base. These may need replacement. Also, reach into the part the flapper rests on and see if it is smooth, it may be corroded or have a little junk on it. This would keep the flapper from sealing. The part the flapper fits into also may have a seal. The water runs because some water leaks out, and the float drops. It then turns on the fill valve to top off the tank. For either of these (and there may be other potential things that could cause it), there are usually readily available fixes.

Be wary of any of those tablets, or other stuff that you may place into the tank to help "clean" your toilet. Most of them contain chlorine, and especially if the toilet doesn't get used often, will really make a mess of things in there because the concentration gets very high.