Calista, it's likely that the various facts you cite in your question come from the lives of several different men named Alexander Mullen/Mullan/McMillen/etc. Those first and last names are not unusual, so it stands to reason that there were multiple people by that name in Ireland, Scotland, and New England in the 1600s and 1700s. It's rather common for people to try to patch together a collection of facts from people who share nothing more than a name, and as you say it can create a tangled web.
The profile you linked to in your question (Alexander Mullen born in 1643) is unlikely to represent a man who emigrated to America from Ulster circa 1718 or later (he would have been 75 years old in 1718; men that age seldom emigrated). And the man who was married in Dublin on 14 August 1716 (the date on the marriage record you linked to) is very unlikely to have been an Ulster Scot who later went to America, since Dublin is not part of Ulster, and the marriage does not appear to have been in a Presbyterian church (Ulster Scots were Presbyterians). The man who was imported as a prisoner to work in the Saugus Iron Works would have arrived in America in 1650 or 1651, so he was born well before 1643, and he is much more likely to have been from Scotland than Ireland.
As for the names, remember that few people could read and write in the 17th and early 18th centuries, and consistent spelling was a concept that hadn't yet been adopted. Names are spelled in diverse ways in the records (sometimes the same name is spelled differently within one document), and there's rarely any significance to the spelling variations we see.
If you've been collecting records about people with this name, I suggest that you compile all of the records and facts in a list -- document each record you found and what information it contains. Don't think of the facts as relating to one person -- it's just a list of facts about people with this name. For those facts that have dates, you might want to sort them in chronological order. Some of us use WikiTree free-space pages as places to compile collections of notes like these to use for reference.
But your main interest in this name probably relates to an ancestor of yours. What do you know about your ancestor and how do you know it? You haven't added your ancestry to WikiTree yet, so I can't tell what information you have about the generations that sit between you and Alexander... For best results, work backwards in time!