There's a big Caribbean population out here in Cambria Heights/Queens Village, so I think it's a good bet. (Compare to the flag of Trinidad and Tobago.)
My understanding is that the X-in-a-square you sometimes see painted on a vacant building warns firefighters that the structure is compromised and should not be entered unless absolutely necessary.
On the other side of this wall is the Little Sisters of the Poor's Queen of Peace Residence.
Repossessed by the Federal Housing Administration; acquired by the city's Housing Authority
This Art Deco structure (wider shot here) was built in 1933. Babe Ruth served in the 104th Field Artillery, a unit of the New York National Guard, for a few years in the 1920s (photos here), but that was before the regiment moved to this location. On a related note, you can see Ruth's World War I draft card (from back in his Boston Red Sox days) here.
surround an old water storage tank that was built by the Jamaica Water Supply Company and is now part of the city's unused groundwater supply system.
I've seen several similar paintings in other parts of the city, and I finally figured out what they are: rangoli designs! Rangoli (known regionally by other names, including kolam, alpana/alpona, aripan, and mandana) is an ancient art form, traditionally practiced by women, that originated in the Indian subcontinent. You can see more examples here, and you can watch the "world's largest alpona" — several acres in size — being painted on a major thoroughfare in Dhaka, Bangladesh here.
The plaque relates the legendary account of General Woodhull's death, claiming that on August 28, 1776, after having been captured, he "was mortally wounded by a British officer near this spot for refusing to say God save the King".
According to the AIA Guide to New York City, this "large, freestanding, elaborately ornamented Italianate house is a remarkable throwback to the area's 19-century roots."