What to do for my 15-year-old dog's tumor, arthritis, and ear lump?

Poor guy. That is a lot to consider. Here is a good treatment plan.
Tumor on belly- I would recommend getting this removed surgically and then sending it off for analysis so that you know if it is benign or cancerous, and if any further treatment is recommended.
Arthritis- you can attempt to manage this with over the counter Dasuquin. This product works very well for mild arthritis symptoms. But if his arthritis symptoms are moderate to severe, then he will respond better to prescription medications and/or arthritis injections (Adequan) through your vet.
Swollen elbows- I would really have to visualize this in order to give you recommendations on care. If you are trying to describe calluses on the elbows, then getting Dixie soft bedding can help this. Calluses in general however are not harmful or painful to your pet, because they are the body's response to laying on hard surfaces. This is a way for the body to protect itself from cuts or abrasions developing on the skin.
Wart-like lump in ear- Warts are quite common in older dogs. They are usually benign however and don't require treatment unless they start to bother your pet Dixie or if they ulcerate and/or bleed. If the wart does become a problem then surgically removal is how you would resolve this.