How to test my understanding of an academic paper?
Academic papers deal with the state-of-the-art of the field, either pushing it or reviewing it. So, to fully understand them, you need a deep knowledge of the field.

Now, "fully understanding" them might be a bit broad statement. The key of the paper are the problem and the solution, but I put more emphasis on the problem. For, if you are able to understand what the problem is, why is it hard, its background (where it stands in relation to related work) and implications (how future problems are derived from it), you probably have enough subject knowledge to digest the whole paper. The solution is important, but not so much on a fundamental level as on a conceptual, i.e. you don't have to understand every line of a proof to get why a theorem solves a problem.

So, the first step is understanding the problem and the second "getting" the solution. If you want to be more strict with yourself, ask yourself after reading a paper whether you are able to think about the boundaries of the problem or solution, i.e. what could be done to improve them or what could be derived from them (not minding at that point if that is feasible or not).

PS: If you really are doing research in a field, you need to analyze the paper on deeper levels (check the references, the experimental setup, remember the proof from above and the one you read in another paper 3 months ago, etc.), but at your level, the above seems more than enough.

PPS: I don't see a problem with you joining those "seminars". Ask the professor if you could participate in some of them, at the beginning only by being present and listening. See if it suits you. Once you get the hang of it, you can actively be a part of the discussions. It may be hard to keep up, but that shouldn't discourage you. And you shouldn't strive for the level of understanding the graduate students are at, that'll come with time.