Then the next set of guest came, drank it, which was furnished by the rental, and then got injured?

INJURY:  What about if a tenant or tenant's guest is injured inside the condo? 

If one tenants property is damaged as a result of the negligence of another tenant, if someone is injured while visiting one of your tenants or if someone is injured driving home after drinking heavily in one of your tenants units and sues a renters policy will likely respond respond. 

That lawsuit is a claim for fraud, and that’s what fraud typically is...a misunderstanding and someone being “injured” and wanting to hold the other responsible for it.

If a sub gets injured on site does that fall on me as homeowner or acting GC?

Typically speaking, having all property in one LLC does mean that it can be reached by judgment creditors (people who are injured).

Also, if someone gets seriously injured on the property, having a higher liability limit would be beneficial (Think about someone being permanently disabled, for example.)

If someone injures themselves and sues, they will be suing the LLC and not you personally.

Common eg. that many people quote: Let's say the tenant is injured in the property and decides to file a lawsuit against you does umbrella insurance help in this scenario?

Quick note - regardless of term if you allow dogs or the tenant has one undisclosed and the dog bites someone or another person's pet the attorneys for the injured party will name the dog owner to the suit (obviously) but also name the homeowner to the lawsuit even if the event occurred off site such as walking the dog.You can say that's wrong all you want and I'd 100% agree - this is how it works.Your first layer of protection here is the tenant having renters insurance (that does not have an exclusion for dog bite or an exclusion for the tenant's dog breed).