I advise getting the battery tested before spending any serious money it. Any auto electrician will be able to do that at little or no cost. Apparently even Halfords, though I am not a fan of the company.
Bear in mind what I mentioned about coding a new battery to the car, and if the battery fitter does not know what coding is buy the battery from somebody more competant.
I have no experience of Lion brand batteries, but other folk here do, and they condemn them. Buy a well known brand such as Exide or Varta amongst others. It will be more expensive, but worth it in the long run.
Only once you have a proven decent battery is it worth investigating the other electrical faults, if they still exist. You may find they have disappeared.