A further question: Did any Priests or significant religious figures follow the armies of any Crusade, to act as a rallying of support, to organize things like Mass, etc., or to deliver the aforementioned rites to dying?

I can't comment on the development of the sale of indulgences in anywhere near enough detail to answer the second part of your question, but I can provide some context to the first.

Firstly, the idea that crusaders would die far from a priest is absurd. Many priests went on the First Crusade. Most of our eyewitness accounts of the crusade were written by priests. Fulcher of Chartres, Raymond of Aguilers, and Ralph of Caen were all definitely priests, while the anonymous author of the Gesta Francorum has been widely debated but was probably also of some sort of religious background. There were also numerous papal legates (think ambassadors...but more medieval) joined the crusade with Bishop Adhemar of Le Puy taking on a prominent leading role. This is to leave aside the many personal clerics and confessors that major nobles would have brought with them (Raymond of Aguilers was actually attending as a cleric to Raymond of Toulouse, one of the crusade's leaders). There were priests a plenty, is my point.

As to the beginnings of the indulgence as part of the First Crusade...that's a little more complicated. A lot has been written on this topic by theological scholars, and there are aspects of the debate that go totally over my head, so I'll try and keep this simple. Just understand that there is a lot of nuance and discussion that is being cut out here for the sake of simplicity and comprehension.

We have multiple accounts of the Council of Clermont where Urban II announced the the First Crusade, but none of them are 'official' per se, meaning here that they are written by the papacy. The two primary chronicle accounts we have are Fulcher of Chartres and Robert the Monk. There has been a lot of debate about which one is more accurate. Their accounts agree on most of the big points, but have a lot of differences in the details. Most likely both of them are embellishing or omitting points that they don't like, and the truth is a third option, but they're what we have to work with (well...them and a few minor bits of supporting evidence we won't be covering here).

Fulcher of Chartres has Urban II say that anyone who dies while on the crusade will be given a 'remission of their sins', while Robert the Monk has him say that anyone who goes on the crusade will receive the remission. The difference between remission of sins and indulgence has been debated on and off in theological circles, my rough understanding of it (it's some pretty nuanced stuff, and I am not a theological scholar) is that indulgences were slightly better. Basically, if you think of sins like crimes, and indulgence is a complete wiping of your record, while a remission is more like a pardon: you are exempt from the punishment for your crime but you are still recorded as having been guilty of it in the past. There has been a convincing recent argument that whatever the theological nuances of this debate, it's hard to show that actual crusaders would have appreciated the difference, and many might have thought they would get indulgences regardless of official church rhetoric. I will not here that later crusades, particularly the Second Crusade, began a practice of giving out full indulgences to anyone who went.

It is also worth considering here some of the context of the First Crusade. The crusade was partly inspired by the practice of pilgrimage. The task of going on a pilgrimage was a common penance assigned to sinners during confession, and the pilgrimage to Jerusalem was the biggest and most important of the lot. If you did something really bad, the pilgrimage to Jerusalem was the ultimate task to make up for your sins. The crusade was envisaged in part as a new sort of pilgrimage. Traditionally you were supposed to go on pilgrimage unarmed, so the crusade was a sort of armed pilgrimage. In this context, anyone participating on the crusade could be seen as undertaking a pilgrimage to Jerusalem, which would involve a remission of all of their sins under normal circumstances. So while the arming of pilgrims was a fairly revolutionary idea, the fact that crusaders would be given exemption from their past sins was perhaps a lesser change, and not entirely unexpected.

Sources:

Christopher Tyerman (ed.) Chronicles of the First Crusade

Christopher Tyerman How to Plan a Crusade

Thomas Asbridge The Crusades