1
Until indicates when something will happen, begin, or end. Till means the same thing as until. Till is not an abbreviation of until—it's actually older than until—and it should not be written with an apostrophe.
2
Begin, when used as transitive verb, means "start, perform, or undergo the first part of an action or activity." Start, when used as transitive verb, means "cause (an event or process) to happen", or "cause or enable someone or something to begin doing or pursuing something."