Hi Englishman: Here is a stab at some answers to your questions.
You asked, "... is their any real scriptural back-up to say that a set number of people will go from Earth to heaven, or is this just a witness interpretation thing?"
Rev. 7:4 and Rev. 14:1 are the ONLY verses in the Bible that discuss the 144,000 where a specific number is mentioned. In both cases this group is mentioned as being in heaven or with the Lamb (aka Jesus). One can conclude that this 'group' goes to heaven, but the attributes given to them are also applied to the Great Crowd. Depending on one's interpretation, the number 144,000 is either symbolic or literal. The literal is what the Watch Tower promotes, but they are one shaky ground. A symbolic number is far easier to support. Other than these two verses, the 144,000 are never discussed in the rest of the Bible, nor in secular writings by the early Christians (or at least few secular writings, but hardly known or accepted.)
You asked, "Also, how does this “remnant” become aware that they have a calling?"
Important to understand this: The JW anointing process is virtually identical to the rest of Christendom. I professed this calling for over 20 years as a JW. When one reads the Bible and puts faith in Jesus Christ as their mediator, they are adopted into God's family and called a 'son' or 'child' of God. Anointing is the 'spirit' of adoption. This 'spirit' means that your mental and emotional response to this feature of faith is positive, that is you identify with it, and recognize that it applies to you. Simple.
It can be illustrated this way: If you are on a trip with a friend who has the same first and last name as you, say, Mike Jones. Your respective fathers also have the same name, say Tom. A letter comes addressed to Mike Jones from Tom Jones (typed). You and your friend both read the letter together. But, one of you will recognize that the letter is not intended for you, and the other will easily recognize what his own father would say to him. The letter might contain things that apply to both, but it will primarily be directed at only one of you. You, say are the Mike that the letter is intended for, and you will identify with your own father, and respond that way.
This is the best illustration of the Watch Tower premise of how the Anointed know they are such. In Christendon, when you read what the father has to say in the Bible, you respond out of faith and understand that you have become anointed. But in Christendom, they do not make any big deal out of this feature as it is only one way to characterize an otherwise multi-faceted relationship.
The reason that so-called non-anointed JWs of the Other Sheep are so unclear and confused about this calling is that the Watch Tower steps into the middle of that relationship and scares the beejeebers out of them so that they are afriad to respond positively to the Christian hope. As a result, a mystery is created where none ought to exist.
You asked, "Does the WTBTS tend not to persecute these one’s, if they hold views that would be deemed as apostate in others?"
Far from it. One who professes anointing and holds so-called 'apostate' views is often treated with ever greater suspecion and just as harshly as the Other Sheep class.
You asked, "What is the point of this select group, when they receive their heavenly reward what do they actually DO all day?"
Help run the government. Anything from the heavenly mail room, to the conference center where high level executive decisions are made. Building codes, freeway construction, and of course teaching and training the newly resurrected.
you asked, "What is their “raison d’etre”, and are they, whilst alive on Earth, considered as being exceptionally possessing of God-like qualities?"
This is a common JW belief, and becausde of some misconceptions, JWs of the Other Sheep will often see 'better' qaulities in those professing anointing, but it is more like a placebo effect. They believe they are better, so they see better things in them. In truth, and even in WTS literature, anointed are technically no better than anyone else, they merely were lucky enough to win the Big Spiritual Lottery in the Sky.
Amazing