Is this a steam system?

Yes, it's steam. A bit loud, but very effective.

Maybe it can be retrofitted with an automatic water draining system?

If the water in the sight glass is clear, then there should be no need to drain two buckets of water each week. Did someone tell you need to do this?

You should flush out some water into a bucket until the water runs clear. There will always be rust in the system due to the cast iron pipes and radiators. Some rust is fine, but you don't it to build up over a long period of time. Once a week is probably too often. Every 2 -3 weeks if fine. If you did it less often, I don't think it would be a problem unless the water was unusually dirty.

There are automatic filling systems, but not for draining.

Yes, the previous owner instructed me to do it once a week. Every day when it's really cold she said.

The water never runs clear. It's very red brown.

The Furnace is 20 yrs old but the pipes are probably well over 100 yrs old. The house is 150 yrs old. Does one ever need to replace a radiator system? Not that I want to, just curious what the lifespan of steam radiators would be.

I claim no expertise about that system. But rusting occurs only when "fresh" oxygen is introduced into the system-- and the additional water does that. My idea is that so long as the rust causes no operational problem, draining it and refilling causes additional rust in the system. That is elementary chemistry.
I defer to those who claim expertise.

add some squick follow directions on can. Drain the mud legs once/month at most. I'm surprised there's no drain in the basement, that's unusual.

a steam system is somewhat open so you never have all the oxygen removed from the water. It will get rusty, but it shouldn't be that dark and the sediment should collect in the mud legs and be flushed out when you drain the water - typically a gallon or so, then the water should clear right up, if not, I'd flush the entire boiler, add the squick to bring down any remaining sediment, and then start a monthly draining. It should not need to be done more than that.

If your pipes are banging and making noise, your system may need attention - esp. the air valves on radiators and mains, pressure setting - shouldn't be more than 1 psi.

I won't say much except for that you should refrain from using fresh water so often. And, also check if there is any rusty pipe. I think that there is a rusty pipe issue. That you may have to change.

A properly operating steam system is an excellent heating device. You should not have to be doing this and you may be doing more harm than good. You need to find a professional who knows steam heat and get him in there to to identify issues, correct them and instruct you in how to live with your current boiler. Burnham makes good steam boilers.

I suspect with all the clean water that has been added by you and the previous owner that there is quite a lot of debris in the system. A properly operating steam system should have an auto fill device to maintain the water levels. Fresh water has all kinds of chemicals in it. When you heat the water many of those chemicals will leach out of solution and coat the insides of your system. That will/can reduce heat transfer and create hot spots in the equipment. Get a pro in there. Today would be good!

Oh, and one other thing. If you try to find a pro, be aware that not just any heating contractor knows steam. Make sure you ask specifically for an experienced Steam guy. There aren't that many out there.

Here is a book you should buy and read. I have never read it, but all the reviews say it is excellent.

Here is a link that might be useful: The Lost Art of Steam Heating

HVAC is not my trade. But I have read some of what Dan Holohan has written and it rings true with me.

I know Dan. He is a fine man and certainly a top hand in the industry. His books are excellent. You've had a system that hasn't run properly for X number of years. Read the book but hire someone familiar with the issues of steam.

Here's a thought. Have you considered installing a drain of some kind? Wouldn't something like a condensate pump work for this? Stick the pump in a bucket and pump it on out through a hose?

I would do it just to avoid hauling water up the stairs, even if it's monthly.

Keep in mind I know ZERO about this stuff!

My parents have a similar system. They don't drain the water every week...every few months.

There is an "auto-fill" device you can add on that will automatically maintain water levels by refilling it. I'd add one. You would still need to drain it.

A new furnace is A LOT of money...particularly a large one. If you just purchased an old house, you are bound to finds things that have to be fixed/changed. I wouldn't borrow trouble by replacing the furnace in the winter. Wait until your next big rain and see if there is any flooding/leaking anywhere. Have a home energy assessment to see if you need new insulation. Check for rot or bad wiring. There are a lot of things to think about before contemplating an expensive repair that isn't really necessary.