If below is of any assistance...
Is there any formal way to pray to Amitabha to wish for the well-being of others or a specific person's endeavors?
There are several things to be looked at in this question...
a. Strictly speaking, in Pure Land, no. Why?
Buddhism has no conception of a theist version of 'prayer' and the act of 'praying' in the sense of where the total & ultimate source of one's good and being lies in the object that one petitions to, external to oneself with connotations of one being weak and helpless and mostly motivated by fear and ignorance. Buddhism counters this by positing a Buddha potential that is already in all of us, that a realised Buddha and sentient beings have a thing in common: the Buddha nature. The difference? We allow ourselves to be continually mired in the basic threefold root defilements of craving, aversion & ignorance. So, one can notice a two pronged version of reliance here: one with self independence and liberation in mind and the other positing a continued enslavement to an external source outside of oneself. The Buddhas merely point to us the road but we must do the walking, isn't this a model of reliance based on the first?
b. But, what is available and readily practiced is the practice of making aspirations or some would term it as 'vows' where one gets to read or hear stuff like 'May all be well and happy' and so forth. It's also quite akin to companies that have a mission & vision statement in their company guidebook as a kind of a direction guide as to how the whole enterprise would move and have their operations. If it may be summed up, the purpose of doing this is perhaps fourfold: firstly, to bring forth a resolute mind for an endeavour that h/she is pursuing in this spiritual path; secondly, to rejoice in the merits & goodness of others; thirdly, to bring forth a wholesome & equanimous mind based on the Four Immeasurables at all times and fourthly, to transform and transcend one's own conditions in life. So do you see how this form of aspiration practice is based on firstly tapping into and working on the Buddha potential and secondly, based on the mind of Right View?
c. If one wants to know where does all of one's 'blessings' and 'curses' arises and ceases from in life, one has to study, contemplate and realise for oneself on the Buddha's simple and extensive teachings of karma and its related subjects. When this is well understood in its proper sphere, the question of 'prayer & praying' does not arise for one. In one teaching, the Buddha teaches us to take refuge in one's own karma/action. In the third of the Threefold Pure Land Sutras, 'The Contemplation of Amitayus' text, the Buddha lists down what one can accomplish with one's own karma, 'self power', coupled with reliance on Amitabha's 'Other Power', the offer of Sukhavati to continue the perfection & realisation of the Path & Fruit. So, it's a two pronged approach of reliance and self effort: like a child & parents, the ultimate goal ending with self independence. One can google on how karma is viewed, taught and practiced in the Buddha Dharma as I wish not to flood this simple reply into an encyclopaedia.
d. It is mentioned in many scriptural texts on the 'benefits' of practicing reciting and contemplating on the names of Buddhas & Bodhisattvas or even mantras but really, in the end analysis, it comes back to practising these with understanding the above points to truly reap the 'benefits' as intended instead of degenerating into a superstitious and adventitious attitude and practice. Likened to a constant pouring of fresh water into a cup of salt water until the salt water looses it saltiness, hence for us, with the aid of Buddha Dharma practice, our circumstances in life can change for the better. That's how, to put it crudely, one 'prays' to Amitabha for 'help' in short.
e. But having said all of these, nothing stops anyone from treating Amitabha like any other mundane worldly deity for callous mundane propitiation purposes but from one Pure Land perspective, doing so will only generate one mundane blessings & connection but is not in accord with the actual intended scope of why and what Amitabha practice is for in the ultimate analysis: the perfection of the Bodhisattva Path for Buddhahood. This is like one purchasing a car to transport goods and people from A to B which is what it is intended to be but there are those who use it to drive recklessly and engage in dangerous racing. In one Discourse, the Buddha mentions on how people who grasp wrongly on the Buddha Dharma are like those who are holding a snake from the wrong end only to end up getting bitten. It is not that the Buddha Dharma is capable of harming one but one's own wrong grasping instead.
Also are there a variety of verses that are used as prayers?
Yes. It varies from tradition to tradition and too many to mention here. It can be a whole round of reciting the name of Amitabha for a mere 10 to 108 times to simplified & extensive aspiration verses.