If I normally use a fresh chilli pepper but decide to use the ground version, how do I convert for measuring the amount of ground? For example, 1 fresh pepper = 1 heaped teaspoon ground pepper.
It doesn't work that way because different chilis give different heat, you have to work off the result you want, i.e. how hot you want it. One fresh Jalapeno is pretty mild, one fresh habañero will light you on fire! There are different heats of chili powder depending on the type or blend of chilis used, from paprika, which is very mild, to ground cayenne, which is medium to ground hot chilis of different varieties. One teaspoon of each will give you a very different result. One teaspoon of paprika is milder than 1/8 teaspoon of a hot chili powder.
I suggest you get a chili powder which is right for your taste and vary how much you use depending on the dish. 1/2 of a teaspoon is a reasonable amount to start with for an average size pot of food, you can then keep adding 1/4 or 1/2 teaspoon until you get the heat you want. Just remember to let it cook for a few minutes to let the heat come out. Once you do this a couple of times you'll have a good idea of how much to add in the future.
Fresh pepper/chili and ground pepper/chili are not particularly interchangeable.
For example: (sweet) paprika is essentially ground Bell pepper, but it is not a normal substitution to use replace Bell pepper with x teaspoons of paprika.
Additionally, peppers range in size substantially. A Thai Birdseye chili would only yield a fraction of a teaspoon when dried and ground. A bell pepper is probably more likely to yield a tablespoon or more, depending on the drying process.