This sentence is a nice, intricate example of layered PARALLELISM.

Here's a schematic of the sentence:


One parallel list is of the OBJECTS that the sunbird has:
1. colors
2. patch
3. eye

The other list - relevant to the underlined portion - describes the "four-and-a-half-inch animal":
- found...
- and resembling...
It's ok that one is a past participle and one is a present participle. They both give us modifying information about the same noun - they are functionally parallel. They don't have to be structurally identical.

A. found in the Philippines and that resembles
Here, "that" is not parallel. There is no other dependent clause beginning with "that" for "and that..." to match with.

B. found in the Philippines and that, resembling
Same "and that" problem as in A. Turning "resembling" into a modifier does not fix the problem.

C. found in the Philippines and resembling
Correct! "found" and "resembling" are both modifying "animal."

D. that is found in the Philippines and it resembles
If we say "that is found..." we must say "... and that resembles." The word "it" makes this an independent clause, not parallel to the dependent clause.

E. that is found in the Philippines, resembling
Here, we have a series of "stacked" modifiers. "Found in the Philippines" and "resembling a hummingbird" are both ideas modifying the sunbird. Two such noun modifiers should be put in a parallel list.

The answer is C.