If you have no idea what your tiel died from I would just toss whatever you have at the moment. You could disinfect and there are a couple good threads about disinfecting if you use the search function but it would probably be easier to just toss the things you have and buy new ones.
The 22X13X12 is way to small and if you used it for your tiel it was way too small for him too incase you decide to get another tiel. I'm guessing it was a parakeet cage sold at a petstore which are usually pretty small even for a parakeet. I think and correct me if I'm wrong lovebird people that the min for a lovebird is 24 by 24 by 24 or something along those lines.
Lovebirds are maybe twice as big as a keet and I think an english budgie can beat them in size. Lovebirds are a bit stockier when you look at them though and that beak is an upgrade.
Any new cage will come with food bowls, if you have dowel perches don't bother disinfecting them just toss them, the rope perches are good and perches made of natural wood are great too. You will need lots of toys for them to play with and a playstand would not go amiss.
I don't know exact food requirements but a good pellet and lots of fresh greens and veggies are always pretty standard across the board. I use TOPS, Roudybush, and I'm working on converting from Roudybush to Goldenfeast Pellets since I don't like what is used in Roudybush(salt content). In the diet section of the fourms there is a sticky by MonicaMc that has a good list of safe fresh foods.
Good luck on your new addition! And I am very sorry for the loss of your tiel. Hopefully some knowledgable lovebird people will chime in. (Dally where are you

)