Dummy - a few germs are good for them. Hell, I probably didn't wash my hands every time I picked up a dummy and TBH both my children have put things far, far grosser than dirty dummies in their mouths.
The food - depends on the food. We don't let them have juice and sweets and other processed foods but if their Aunt wants to spoil them it's not the end of the world. It's nice to have extended family to spoil you. I draw the line at pork but no-one in my family would go there anyway.
Teasing - I'd bite their heads off if they called my children names or give my children a few names of their own. Or if I was in a more tolerant mood use it as a teachable moment about the ways in which we shouldn't talk to others.
Older children touching the baby - if they were sick I would offer them a quiet place to rest or pop a DVD on and ask them not to touch the baby. If they weren't sick I would let them have as many cuddles as they wanted on the floor to minimise any risk of dropping.
Disciplining my children - please, please discipline my children for me if you see they need it. It works so well when someone else helps out.