Isn’t it true that Harry was given the title “prince” by HM on the day he was born and that the title is not automatic w/o HM’s bestowal ?

As per Letters Patent issued in 1917, Harry’s status as a HRH Prince was his automatically at birth due to his being a male line grandchild of a monarch, same directive used for princesses Beatrice & Eugenie, and Princes William & George.  The same letters patent were what made Elizabeth and Margaret Princesses from birth.  (Charlotte and Louis getting their royal status in a seperate Letters Patent in 2012) 

Louise and James legally are also entitled to use the HRH with the titles princess and prince respectively, even though their parents (the Earl and Countess of Wessex) asked and The Queen agreed for the younger two to be referred to by the styles used by children of an Earl. Sophie has said of her childrens titles a number of times that a formal denial of their right to the HRH would have an adverse affect on everyone entitled to the same status as grandchildren of a monarch, she has also said that when James and Louise turn 18, she will not stop them from asking to be referred to by their correct titles.Legally The Queen could revoke Harry’s title as a Prince, but she wouldn’t because it’s never been done before, also remember that her father reconfirmed his elder brothers status as a HRH Prince after the abdication in 1936, so there is precedent for removing someone from the senior royal family without revoking their princely status. 

Harry was conceived a Prince

In the UK, male-line grandchildren of the monarch are, indeed, automatically born princes and princesses under current rules (established under George V).  Even Prince Edward's children are actually a prince and princess under those rules and can decide once they become adults whether they want to use those titles.

In other words, Harry was born a prince and royal highness. In theory, the Queen could deprive anyone of a title, since the monarch is "the fount of all honour".  However, since even Edward VIII remained a prince and royal highness after his abdication, it's hardly likely that she would deprive Harry of the status to which he was born.  He's done nothing to merit it.

The Queen was not the first person to visit William's children. His parents-in-law visited before the Queen did.

Your envious resentment of Harry's wife is both sad and juvenile. However, as I said yesterday, it's also so common and typical among less fortunate women like you as to be boring.

It comes automatically with birth.

The whole system should be abolished 

Yes that's true but not for William, William is a Prince by blood on his father's side but neither of Harry's parents had/have royal blood so he would have had to have been given the title or allowed to keep it whenever it was that they found out who his biological father was.

Harry, like William, was born a Prince but I think, without looking it up, HM 'could' remove it.   However it would need to be something REALLY serious for her to do that I'd suggest.   

I don't know about being the first to visit a new royal baby (not necessary a new heir) but that hasn't been the case with recent royal births.  Most have been presented to the world, on the steps of the hospital where they were born.   No sign of HM there at the time.

The Queen theoretically can remove any styles and titles, but there is no suggestion she would do so in the case of Prince Harry, who is the son of a future king.  He is 'automatically' a prince because Letters Patent already existed to that effect when he was born, but the Queen could have varied that if she wished. The first relative to visit was Prince William. What has been removed recently are honorary titles and positions that Prince Harry held in the military which are nothing to do with his official titles.

No, he was  born the son of a prince of wales, he is a prince from the moment he is born, just like his brother wlliam.

The title was bestowed on Harry automatically according to existing letters patent that gave princely titles to every legitimate child of a monarch, and every legitimate child of the son of a monarch. Special letters patent were required to stop Prince Edward's children having princely titles. 

No, it is not true. Harry was BORN a prince, his father, a prince, his grandmother the Queen... that is how it works. One is either BORN a royal, marries a king or prince and assumes the titles of her husband, (for females only), or bestowed one by the monarch. It is rare for a person to be bestowed a royal, the more common way being a royal is through birth or marriage,(females only).

In the UK, a royal is the offspring of the monarch, the monarch's children, the monarch's grandchildren, and the children of the eldest of the Prince of Wales.  Other realms do not cut off the royal title by generations and a prince or princess are the children of the monarch, or prince.

There are many documents about titles here:

https://www.heraldica.org/topics/britain/prince_hi...