There were never any serious injuries or lawsuits. 

(And to add insult to injury, they expect your Application to be handed in by next month, otherwise they say you'll FAIL forever thereafter to receive such a generous prize from them?)

As a former personal injury attorney (Illinois, not Massachusets), I can tell you that if they sue, they will name everyone they can reasonably identify.  

I am concern about the personal injury liability issue and express the concern to my tenant.He express to me he really want to do this job and he is willing to sign a personal waiver if I let him to do fence replacement. 

I love what I do, but I know it won't last forever and there is always the risk of an unforeseen injury or underperformance that can hinder my earning ability.

Do I need to fix it right away to prevent personal injury (sharp glasses) or property lose, since it's the front window?

It has a higher premium due to higher injury risk.

Do I need to get a landlord liability insurance for tenant injuries and claim for my rental property?

Adding insult to injury, the house I bought with the refinanced money is not very profitable either.

I do not know what the situation is in Indiana but I suspect the authorities do not smile on negligent landlords especially if negligence is revealed in an actual fire with damages, injury or even death.