It is possible, especially if you don't use a mainstream brand salt.
I would worry about this as a last step and only if dino's are confirmed. It's possible they are dino's but normally they release gas bubbles and are stringy.
They can, but they are normally removed by the ion resin. If your resin isn't packed tight enough some could get through even brand new resin. I would expect 0TDS from a brand new RODI system. Even 1 TDS doesn't sound right to me.
If you aren't using a food grade storage container it can also cause chemicals to leach into your freshly made RODI.
Food can also be a source, but if your tank sitter used the same food you did without the problem, that can be eliminated.
Nothing wrong with tap water. Many of us have tap water clean enough to use in reef tanks. RODI provides a little peace of mind and eliminates a variable so it gives us less to worry about.
My tap water has low enough levels of copper, nitrate and chloramine that I could use it in a bind.