To solve this you need a good plummer who also handles outside water plus $$. Typically they will install a drain pipe all around the basement, either inside our outside the wall plus a sump pump to carry the water out.

There might be simpler solutions to get you part way there, but engineering is the way to get a dry basement.

The goal is to get any water enclosed in a pipe and routed to a method of discharging it. Your picture is not clear enough of the entire basement - but it is definitely a strange setup (but worthy of the Roman aqueducts) and eliminates usage of the basement. Agree that you will be cutting up concrete and installing some piping and certainly a sump pump, whether you need a full interior perimeter french drain system or exterior footing drain tile is yet to be determined.

There is no way for us to answer this you need to talk to an expert on drainage issues but I would not be having water drain into a basement ever but to fix this is going to be expensive but IMO it would be worth every penny. If you want any help here we need to see alot mor eof the issues both inside and outside.

Wow that is a problem that should be addressed. If it's possible, have a contractor who is an expert in drainage around homes come in and give let you know what has to be done and an estimate. To me, this is a health issue also. I say "if it's possible" because contractors seem to be so busy these days.

I think that @Yvonne Martin is right, although we can't see the entire issue.

Usually the solution is cutting the concrete to put a covered perimeter drain that goes to a sump pump. My guess is those pipes are weep holes from a previous - much less sophisticated - attempt to do something similar.

There are contractors who specialize in doing this. Make sure you are also addressing getting water away from your foundation as much as you can. That involves gutters, downspouts, grade that goes away from the house, etc.

You'll likely have to put in some sort of french drain or similar system in your yard that will pull water away from the house and drain into the street sewer grates. I think that's something a contractor and a plumbing sub could do for you and then you could close up the holes that lead to the basement. Get a couple of quotes.

I used to live in area where all the homes were older and had similar issues. Almost everyone ended up doing French drains. The good news is that if everyone around you has the same problem there should be local contractors who are familiar with the issue and know how to fix it. Start getting bids and hold out for the one with the best reputation even if they're not the lowest price. The other bids are just to make sure they're not way out of line. If this has been going on for almost 100 years I guess another six months won't make a difference.