Yes you can use that word at the beginning of a sentence, For example, "Regarding ___, I think..."

Regarding the dance, can you come tonight? Regarding John Smith, should he win the prize? Regarding the other day, it was not correct to speak so loud. Regarding that other matter, what do you think?

Yes, you can begin a sentence with: 'Regarding... 'With regard to .. 'As regards .. NB The one phrase you can't use here in 'With regards to...' . Even native speakers make this mistake.

Often, you don't need a special word to change or introduce the topic. When you do, you can use 'regarding', but it's quite formal. A more informal way to introduce a topic that might be unexpected is "you know". "You know that dance tonight - will you be able to come?" or "About" "About the dance tonight - will you be able to come?" or "We were talking about", if it's something that had been spoken about previously and you are re-introducing it.