HI there, here are some simple responses to what are actually complex questions followed by a dash of my own observations about immigration generally for a similarly situated person.
1. Is it feasible to get refugee status in my case?
A positive Convention refugee fits into this description, and the threshold for a positive decision is more than a mere possibility - a low bar, but it requires evidence:
96 A Convention refugee is a person who, by reason of a well-founded fear of persecution for reasons of race, religion, nationality, membership in a particular social group or political opinion,
https://laws-lois.justice.gc.ca/eng/acts/i-2.5/section-96.html
Look up Internal Flight Alternatives as this CR consideration blindsides some people.
2. Does anyone have a similar experience and is willing to share?
I've spent a lot of time over the years with all sorts of immigration matters, but fundamental to immigration is that every individual has their own story. Opinions about what will happen are over-priced at 10 cents a dozen.
3. Are there any consequences for applying for a visitor visa in the future if my parents get rejected?
When someone makes a claim to CR status they get a Conditional Removal Order. The condition is that the Order is erased if they're found to be CRs. If the claim fails then the Order comes into effect. It's not impossible to receive another TRV (after their departure) but it becomes less straight forward for anyone that was the subject of a removal order. There's a thing called an Authority to Return to Canada (ARC), but that's another complexity and another deeper exploration.
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All righty then:
I think this site is best used by collecting questions that a person can ask a qualified immigration attorney.
Canadian immigration law, policies and procedures are complex and rife with the potentially unintended consequences. A great lawyer knows the pitfalls, potholes and means for remedial actions - they're rarely cheap but in my experience their credibility within the differing processes can swing a case. A good lawyer's cautions are as valuable as their actions. They're often engaged after some misstep has happened so if one is hired, it's best to do it right from the get-go.
Some things to consider is Canada's tradition of coming up with special measures for foreign nationals at a time of crisis; other post claim (if there's a negative CR finding) programs like H&C/PRRA, and how to best time the initiation of any of the proceeding things that I mentioned.
You know, there's nothing so important as someone's health and safety. As simple as your query is, you've demonstrated forward thinking and this is what you'll wish to keep doing. Immigration's foundation is designed to be reasonable. The reputation of the Department is that they're better with a crisis than they are with their daily lines of business. I mean here that their actions AFTER a Russian invasion could swing wildly from how their policies work today. You can wager that they're planning some response should there be an invasion.
What should you do? In my opinion, you should engage the very best counsel that you can afford and collect questions continuously so that you can leave your lawyer's office knowing what he or she is doing. Immigration is self-described as having "streams." There are economic, protection and humanitarian streams (permanent) - visitors, workers and students (temporary) - blah, blah, blah except for this, people voluntarily jump into one stream or another. So, look before you leap.
Good luck
