Simple answer yes you can, they are different viruses that cause common cold, flu or Covid. All SARS family but different mutations
As I understand it, from reading research from the old Common Cold Research Unit in the UK many years ago, colds are made up of various viruses. Some colds are caused by types of coronaviruses. If you are only protected against Covid, you are unlikely to be protected against the majority of common colds.
It makes sense that wearing a mask & washing hands often should drastically reduce chances of getting a regular cold or even the regular flu for the most part. Neither of these is as stealth as the Covid virus.
Probably. But as the above states, less likely than other years if you're taking the precautions. Apparently South America had a low flu season because of the precautions against covid, and that should also apply to colds, but as we can all attest, colds seem to arise out of nowhere. They've been around for so long and have mutated so much, whereas covid is new to humans. An interesting sidebar, though, is that the Russian Sputnik vaccine and AstraZeneca vaccine and some others may be using the cold virus, which is also a corona virus, as their foundation for vaccinating against covid. If these vaccines are doing that and they actually work, I wonder if we get vaccinated with those vaccines whether there will be any additional gain against colds. I suppose it's also possible that the Moderna and Pfizer vaccines might help against colds because again, while they don't use the old technology of using viruses to inoculate against viruses but instead use RNA to tell us to make antibodies that maybe since they target the spike shape protein that it might again prove to have some benefit against all corona viruses. Don't know, but it's interesting.
Most articles on the topic say that if someone masks all the time when they are out, and their mask fits properly, and they practice social distancing and wash their hands properly, their chances of both colds and flu will go down. Nothing I've seen promises perfect protection from getting a cold, but evidence shows that the numbers go down where everyone is masking. Colds and flu are respiratory viruses, like Covid, so it makes sense that measures to block their spread work the same way.