For my science fair, I am confused on if I should write, "daphnia", "daphnias", or "Daphnia" regarding to the species, especially multiple of them.
Is there a certain time to use the word in upper case, italics, etc.?
Daphnia is not the name of a species, but of a genus. Genus names conventionally have the form of singular Latin nouns, and lack explicitly pluralized forms: some other examples of genus names are Homo, Canis, Felis. In scientific contexts, genus names are written capitalized and italicized (see e.g. this APA style guide blog post).
Although genus names are singular in form, you may see them used with plural verbs or plural pronouns: this is an example of the phenomenon of "notional agreement", which also occurs with other kinds of nouns in English. There are no firm rules about when to use notional agreement.
"Common names" for animals are not standardized. Sometimes a group of animals has a common name with the same form as the genus name: e.g. animals in the genus Gorilla are called gorillas. I have most often seen common names written in lowercase (unless they contain a proper noun or proper adjective, as in "Canada goose") and without italicization. So I would not recommend writing "daphnia" or "Daphnia", but you might be able to write "daphnia" or "daphnias" if you consider this to be a common name for these animals.
There are dictionaries that list "daphnia" as a common noun. The American Heritage Dictionary calls it a plural noun, whereas Collins defines it as "any water flea of the genus Daphnia", using the singular word "flea".
As a common name, "daphnia" might be used as a singular count noun, a noncount noun (singular in form but not in meaning), or as an irregular plural count noun. Perhaps compare "algae" and "plankton". The pluralized count noun form "daphnias" seems to be rare, but not completely nonexistent. I would recommend against using the Latinate plural form "daphniae", but I was able to find one example, in the English summary of an article that was apparently written in German: "Toxicological investigations in an artificial ecosystem. A progress report on copper toxicity towards algae and daphniae".
In the context of a science fair, it seems appropriate to use the scientific name rather than a common name, so I would recommend writing "Daphnia". If you know which species you are dealing with, it would be good to include the second part of the binomial as well; e.g. "Daphnia pulex" (which can be abbreviated as "D. pulex" after the first mention if you need to save space).
In English there are some species which have similar singular and plural forms (species, fish, salmon, etc.).
According to Oxford Living Dictionaries (https://en.oxforddictionaries.com/)
there is only one form of the word in the Singular and Plural - DAPHNIA :
‘A large part of their diet consists of many winged insects, a large assortment of aquatic insects, and some zooplankton such as daphnia.’
‘When they reach a length of 12 mm, chub begin to feed more on small invertebrates, particularly chironomid larvae and tiny crustaceans, such as daphnia.’
‘In addition to fish, other aquatic creatures such as clams and daphnia are used as indicators of chemical changes.’
‘They are not fighting for breath as some people believe, but are instead feeding on the dense clouds of daphnia that gather just below the surface.’
‘Small fish begin by feeding upon zooplankton, mainly cladocera, such as daphnia, before moving onto bloodworm and larger invertebrates as they grow.’
‘Fish are feeding on small light olive buzzers and daphnia.’
‘The fish are still feeding heavily on the prolific green daphnia.'
Also, see some examples from Reverso.context.net:
The daphnia are exposed for 48 hours to the test substance added to the water in varying concentrations.
This classification is based on the fact that the substance is very toxic to fish, daphnia or algae and the substance is not readily degradable or bioaccumulative.
The object is to determine the effective concentration of the substance in water which renders 50% of the daphnia unable to swim.