I have a 6 inch main from house to city Main drain. It takes alot of water from the roof and a drive way drain when it rains. Many downspouts go into the main because of the design of this old house (built in 1927). Assuming the main is root free, should heavy rains going through the system be able to make through my 6 inch pipe?
This is impossible to answer with the given information and the variability of nature. Will it survive most typical rains? Probably. Would it survive a "once in a 100 years" rainfall? Who knows, probably not. Often the cities trunk sewers can't keep up with these either so at that point, your small section of sewer is irrelevant.
The best course of action you could take is to disconnect your downspouts from the sewer line and have them drain away from your foundation so that the amount of rain has no impact on this.
Another wise option would be to install a backflow valve on your sewer so a backup in the cities portion of the sewer does not flood your basement.
Probably. Depending on your roof size and what "heavy rain" means in your area.
This chart says that the capacity of a 6" pipe with a 2% decline (2 ft per 100 ft or 1/4" inch per foot) is 105 gallons per minute. (I can't reproduce the chart here due to copyright)
Heavy rain is defined as being more than 0.39 inches per hour (and violent rain is > 2 inches per hour), so let's say that a really heavy rain is 1 inch per hour.
A 1000 sq ft roof will collect 623 gallons per hour of rain, or around 10 gallons per minute which is well within the capacity of the pipe.
2 years ago this week my city of 5,000 homes had 4-6 inches of rain in 90 minutes during the night and it backed up into everyone's basements. The sanitary and sewer are supposed to be separate but are crossed/broken on many homes (only tested when sold). We had over 2 feet of yucky water, sewage, etc. in our basement.
We have since had a "sewer backup valve" (google it) installed in the sanitary line, right on our side of the city's main, 7 feet below ground. Hopefully it will work. Hopefully we will never find out but it happened here less than 10 years prior as well.
Even if you fix yours, you're at the mercy of the rest of the city.