some of my original codes have disappeared

My think, if when ask for certificate, there is a question about just 2 problems, it can be explaind or you can solve 2 more. BTW when I writen this message and saved I seen other message with my name temporary, now it gone. Bug?

Hi Friend!

however now my codes - the problem of life is simple and hufman codding - have disappeared and in their place there are the codes that I ran later to learn

The site only saves one version of code (for each problem and language) - and it happens only when you click "submit"...

In both cases it seems you have submitted some failing code later, after already solving the problem. So your solution was replaced. There is no way to retrieve it if you haven't saved code locally.

Regretfully the site uses cheap infrastructure and database will bloat if we save all submissions (though perhaps in future we should find a way to do so).

run other people's codes after making mine, without clicking submit

I think if you only run code, without submitting, you are safe, it is not stored and won't replace anything.

I am trying to get certified and I am concerned that this situation could be taken for fraud

This is a correct concern, but as you warned about this situation it is ok, don't worry, please! Your explanation is enough (along with submission log). Real cheaters usually submit dozens of stolen problems, not just two. :)

So proceed without hesitation, just avoid clicking "submit" while testing other's codes. Or at least mark them with different language (e.g. Other) so they are stored separately.