As always, the devil is in the details. How will "mass surveillance" be implemented? How will bad opinions be suppressed? How will misguided officials be blocked?
Even the vague outline you've provided has issues. You can't prevent someone from having an opinion. You can't figure out who is "influenced" vs merely "exposed" (and visible intrusion shifts people towards the former).
You should actually consider the downsides and failure modes of implemented mass surveillance, not "it prevents malicious foreign influence better than my other proposals", because it may be worse than said influence (which does not necessarily translate into control; keep in mind that Georgescu only won the primary and would've lost the runoff had it not been annulled). The world under free information is the devil you know.
I always hold that the problem with mass censorship and state overreach is, they are too powerful and people are too selfish and stupid. There's no good solution, but my prediction is that any drastic attempt to prevent foreign interference will backfire and fail at that (liberal leaders can't use authoritarian tools as effectively as authoritarians). Even Democracy, "the worst form of government except for all others that have been tried", is a better countermeasure; all you need, to prevent anti-democratic foreign capture and ultimate failure, is to preserve it.
I think the definition of what is "anti-democratic" is as hard as the initial 3 questions you pose. If you push second-order ideas, for example by using refugees as indirect fuel for anti-democratic sentiment, is that anti-democratic? The Romanian election propaganda in itself was not anti-democratic, the coordination from a foreign state was. This means that the future of this kind of interference could be a more diffuse approach, or an approach where this is done from within Europe.
Any countermeasure you propose will just lead to moving one level of abstraction, or finding another point of entry.
I do think it's a better idea than mass surveillance, but I believe that the states will see it as harder. It can be that mass surveillance is implemented, and then the states do not know what to do with the data and nothing is achieved.