Accepted answer
Start from what "research use only" actually means, because most of the downstream questions are answered by it. It means no release testing, no pharmacovigilance, no regulatory obligation to you, and no recourse.
Personal-importation discretion varies more than people assume. Several jurisdictions operate a published enforcement-discretion policy for small quantities for personal use of unapproved products; several do not, and treat any importation of an unapproved medicinal product as an offence irrespective of quantity. The distinction is jurisdiction-specific and worth checking rather than inferring from a forum consensus.
Concretely, the diagnostic red flags, in rough order of how much they tell you: a certificate whose lot number does not match the vial; a certificate with no method section; a purity figure quoted to two decimal places with no chromatogram; a testing date that precedes the stated manufacturing date; identical certificates across nominally different lots; and "sterile filtered" offered in place of a sterility test. Each of those is a specific inference, not a vibe.
Regulatory positions on personal importation are published: the relevant frameworks are the US FDA’s personal importation policy in its Regulatory Procedures Manual, the UK MHRA’s guidance on importing medicines for personal use, and the equivalent national provisions in the EU member states and Australia’s Therapeutic Goods Administration personal importation scheme. They differ materially from each other.
One qualification: independent testing tells you about the vial you sent. It tells you about the vial you kept only under an assumption of homogeneity that nobody has tested.
The evidence you want is boring: the same result, from an independent laboratory, across more than one lot, over more than one year.