A:AnswerGo ahead and purchase a new Monitor, you going to in the near future anyway.
Use your old monitor on the device it was connected to in the past and move forward, The new monitors are very reasonable in price now days
A:AnswerYES - there are cables that have HDMI at one end and can go to whatever generation iPad you have, Google "HDMI to iPad" and you'll find whatever specific converter you need here on the BestBuy website itself.
A:AnswerYou could try the following:
Choose Apple menu > System Preferences, click Sound, then click Output. If your computer has only one audio port, choose Sound Output from the “Use audio port for” menu, and then make sure your external speakers are selected.
A:AnswerIf your Xbox has an HDMI output than it should allow you to connect to the monitor. You might have issues with screen size or resolution thought.