Can I Still Be Employed With A Criminal Record?

Yes you can, but the job hunt will be excruciatingly more difficult depending on the degree of crime you were convicted for.

Some jobs will exclude you (e.g. Banks if your crime was one of dishonesty), but generally no, although the job search will be much more difficult, and dependent on the nature of your crime.

Yes you can depending on the type of position you are applying for and what the responsibilities of the position entail; however most employers are very leery of criminals unfortunately and sometimes prejudge you based on your criminal record, and/or the exact crime that you did commit. It's always best to be honest about your criminal history if an employer does ask it.