Normally the active ingredient in toilet bowl cleaners is phosphoric acid at about a 20 percent concentration, but you can get much stronger toilet bowl cleaners that will use hydrochloric acid at up to 25% concentration or more.
Basically, phosphoric acid works well because it will dissolves anything you'd expect to find in a toilet bowl, given time. One thing it won't dissolve is any marks made on the porcelain by using metal tools to clean the bowl, especially aluminum which is particularily bad at leaving marks on surfaces. You can, however remove those marks by using a strong hydrochloric acid based toilet bowl cleaner. When I've done that, I've simply used a small amount of the strong cleaner on a Q-tip to clean off the marks on the porcelain.
The reddish brown discolouration may very well be iron oxide from iron water pipes in your house. I don't think phosphoric acid will dissolve iron oxide, but a strong hydrochloric acid based toilet bowl cleaner sure will. Also, you don't need to use much of the stuff. Go to a "dollar store" and buy a cheap paint brush with plastic bristles (nylon or polyester) and use that to paint the toilet bowl cleaner onto the bowl in a thin film.
Phosphoric acid is commonly used as the active ingredient in bathroom cleaners because it cuts through soap scum quickly and easily, but won't harm chrome. Be very careful using hydrochloric acid around any chrome parts of your toilet because hydrochloric acid will attack a chrome finish. I have several chrome plated solid brass faucets in my building that have had their finish ruined by tenants trying to clean them with a hydrochloric acid based toilet bowl cleaner.
If the active ingredient and concentration of the toilet bowl cleaner isn't printed on the bottle, then you should be able to find it on the MSDS sheet. (Material Safety Data Sheet) Every company that makes chemical products used by the public is required to make an MSDS sheet available to anyone who requests one on each product it makes. That way, emergency responders can know what's in the product so that they know what they're dealing with. If a baby swallows some pink liquid, the doctors at the hospital have to know what's in that pink liquid to know how to best treat the situation.
Anyhow, you can find out what's in most products by using Google to find the MSDS sheet for the product online. I'm thinking that red discolouration is iron oxide from the iron water piping in your house, and you're going to need hydrochloric acid to remove it. You could use muriatic acid. The advantage of using a toilet bowl cleaner with hydrochloric acid in it is that it'll be gelled so that it doesn't quickly drain off the sloped sides of the bowl the way muriatic acid would.
Hydrochloric acid won't hard glass or porcelain. Neither will the much weaker phosphoric acid.