Is there any significance of having received multiple "best paper awards" (in the field of theoretical computer science) when applying for faculty positions after a postdoc? Do the hiring committees watch out for such awards or do they fall into the category of "nice to have but no one cares"?
Best Paper Awards — especially at top conferences — count for a lot in computer science and can certainly help you stand out on the job market. I've seen people introduced multiple times in computer science venues as having won "many best papers awards" or "multiple best paper awards." People notice and people care.
Lots of other things matter as well and will matter more. A best paper awards at a conference nobody has heard of is unlikely to help much. In that sense, I don't think that hiring committees are "watching out for" best paper awards in any systematic ways. But I think it's absolutely normal to note your award winning papers as such in your CV and I think you definitely should. Having your work recognized as among the best at a conference will only help so there's no reason not to mention it.
Depends on the prestige of the conference or journal that you have got it from. If it was a 20 person workshop I would say no but if it was the paper of the year award in a leading journal or best paper in the leading conference in your field then it is definitely an indicator of the relevance of your research and recognition of your contribution and its quality. It is one of the factors that my faculty looks into when hiring so the quality of the publications, where they were published and these awards do matter.