A depleted or nearly depleted battery should be totally recharged and tested. The battery should not be used while the charger is hooked up. Charge your battery following the instructions to the charger. If the charger is working the battery should then have a full charge. Then you can get the battery tested to determine if it needs replaced. If it needs ...
Two ways around this:
For the red one, you can cut a segment out of the terminal so it will slide onto the bolt.
For the negative, you can bolt to the other end of the negative cable.
Another possibility for the red one is to find one of the live wires into the fuse box or even a wire that is permanently live into a relay and connect there.
If the battery is not defective and the charging voltage and current are correct, there is no release of non-toxic hydrogen. If hydrogen is released ,you are breaking down water and it would need to be replaced. I have not added water to a lead/sulfuric car battery in 40+ years; ie. I have not had a car battery release hydrogen in 40 years.