So, just starting out with the Italian language, 'sono spiacente' is a formal version of 'mi scuso'. Sono spiacente means 'I am (very/whole heartedly) sorry' as in something you've done wrong and feel very bad for. While Mi Scuso means 'im sorry' informally, as in sorry (my mistake, my bad, we are closed sorry, oops sorry, sorry ill get you the right pen). The reason we are taught spiacente at first in duolingo is because it uses sono and not Mi, and a foreigner using spiacente shows native speakers of Italian that we are very sorry for our mistake? Is this all true and correct? hahaha
Yes. You can almost always leave off the subject pronoun. There should be no confusion with "essere" conjugating "io sono" and "loro sono" because since it's a stative verb, "spiacente" is an adjective that must agree with the subject, whether the subject is explicitly stated or not.
Usually you can say also "mi scusi" http://fakeplus.com/pictures/jpg/-mi-scusi_20120521112805.jpg
lo sono spiacente ti ho preso quel brutto maglione per il tuo compleanno. Ora finire la pasta in modo da poter pulire la casa. That is how I would use this in a sentence.
I killed your child and cheated on you. I took all your money, and took your dog to the pound. Sorry! If that happened, then dang. what a tragedy. I doubt it but the wise man said: "Give me your money, now get in the trunk." No, just kidding, he said: Never be mean. Always be flux. follow the law, or be a ❤❤❤❤❤❤❤.