What are the standard mental health tests that are available online? Are there standard mental health tests available online with score interpretations? For example, if someone was interested in getting a grasp on their mental condition before seeing a psychologist/psychiatrist.
There's no "standard" on-line test for mood disorders. The only standard one is [semi-]structured evaluation (e.g. SCID-5) by a mental health professional.

With that disclaimer aside, there are some screening tools designed to be self-rated, e.g.


mania


MDQ, e.g. free as PDF/paper form at SAMHSA
a patient version of YMRS is also available: e.g. on psychology-tools.com although Wikipeida says it has an high false positive rate in younger people.
Altman Self-Rating Mania Scale e.g. also on psychology-tools.com. 

depression and anxiety


PHQ a suite of tests developed by Pfizer, officially avaialble at https://www.phqscreeners.com/ There are different tests actually for depression and generalized anxiety; PHQ-9 is for depression; GAD-7 for the latter). They can also be found elsewhere, e.g. GAD-7 on SAMHSA or PHQ-9 on USPSTF; psychology-tools.com has both of them: phq-9 there, gad-7
CES-D for depresion found on http://cesd-r.com/ but also elsewhere (older version).
Zung Self-Rating Depression Scale e.g. on psychology-tools.com and Zung Self-Rating Anxiety Scale in the same place.
for anxiety there exist more specialized tests/screeners, depending on the kind suspected, e.g. social anxiety or phobias, but I don't want to go into a full list. See resources at the end of the answer if you're looking for those.



And here's a more extended disclaimer from one of those, which applies to all:


  The BDI suffers from the same problems as other self-report inventories, in that scores can be easily exaggerated or minimized by the person completing them. Like all questionnaires, the way the instrument is administered can have an effect on the final score. If a patient is asked to fill out the form in front of other people in a clinical environment, for instance, social expectations have been shown to elicit a different response compared to administration via a postal survey.


and from another (PHQ page actually):


  The influence of these biases can mitigated by following up with a structured or semi-structured interview, the gold standard for diagnostic assessment.


There's a longer list of tests on Wikipedia, not all of which might be on-line presently. https://www.outcometracker.org/library/ is an alternative list of printed questionnaires; not sure how long it will be there.  Also these are not all designed to be self-rated; the instruction at top of which page will give clue in that respect. https://psychology-tools.com/ is the most on-line-oriented of these collections.