You did good getting a new battery. Not so good with the acid filling. There are 6 cells working in series. The current has to flow though all six and if one is deficient it severely reduces battery output. At best, you only have 5/6 of a battery and with one cell only a 1/4 full, you may actually have 1/4 of a whole battery power.
You may still have other electrical issues with the bike, but it is pretty much pointless to work on those without battery power.
Your bike will not run without a battery. The alternator won't work without battery power to getting it intiially excited no matter how much you kick the starter lever. And, the coils won't fire the spark plugs without electrical power either.
So, get the battery properly serviced and charged, then move on to checking out the bike electricals. You are probably going to need a meter to sort things out. Digital ones can be had for under $10 these days.
If you or the previous owner at any time reversed the polarity of the jumper cables while getting power from a car, at least part of the charging system has been damaged, for certain. And, this may explain the battery drain over time.
There is information in the FAQ to help you examine and correct faulty charging systems.
Cheers,