In Europe it is a bit complicated to provide you a complete answer. Considering that microalgae are not part of the normal (historic) human diet the introduction of such an ingredient as a food ingredient would require it to have an approved "novel food" status. If you want to know more about "novel foods" follow this link:

http://ec.europa.eu/food/food/biotechnology/novelfood/index_en.htm

There you will also find a catalogue of novel food ingredients already authorized in the EU.

If you would consider the use of microalgae in food supplements than the above does not apply and than it becomes complicated. Food supplements are currently only partially regulated on the EU level. That is there is EU legislation about vitamins and minerals in such products but that legislation does not say anything about extracts or botanicals. That means that each of the current 27 EU memberstates has its own legislation and rules dealing with this kind of products. Since you are located in Belgium I would like to draw you attention to the K.B. of August 29, 1997 "Betreffende de fabrikage van en de handel in voedingsmiddelen die uit planten of plantenbereidingen samengesteld zijn of deze bevatten".

I am somewhat less familiar with the situation in the US, but in the US you have the EAFUS list (everything added to food in the United States). You can consult it here:

http://www.accessdata.fda.gov/scripts/fcn/fcnnavigation.cfm?rpt=eafuslisting

Regarding supplements I think the situation is somewhat less complicated than in Europe.

FDA says the following:

"Generally, manufacturers do not need to register their products with FDA or get FDA approval before producing or selling dietary supplements.* Manufacturers must make sure that product label information is truthful and not misleading.

In addition, the manufacturer, packer, or distributor whose name appears on the label of a dietary supplement marketed in the United States is required to submit to FDA all serious adverse event reports associated with use of the dietary supplement in the United States."

In case of your microalgae this would mean if you have scientific proof that they are save you can use them in a supplement in the US. One major remark though: if you make health claims - e.g. this product is good for your cholesterol - than you risk to get serious problems with FDA if you have not submitted the proper dossier.

As far I know its still just Spirulina and Chlorella in on the market as unprocessed food/food supplement. Because of the fact that microalgal cell wall big chain carbohydrates usually have immun stimilant effect its complicated. I heard in some EU contried they are thiking of banning the Chlorella sp. for human nutrition also. However you can still produce (yes even after 2 years) Spirulina nad Chlorella sp. for human nutrition.

No, but at this link we can see the EU list of (approved) novel food (and see microalgae such as Tetraselmis chuii): https://eur-lex.europa.eu/legal-content/IT/TXT/?uri=CELEX:02017R2470-20200308 .

In the EU novel food catalogue we can see that some microalgae (such as Clorella and Spirulina) are already authorized because they are not considered 'novel'.