Salutations in emails are not absolutely necessary: if colleagues or family members email each other multiple times a day, they are probably going to quickly dispense with any salutation.
But if I am writing an email to someone I do not have an established relationship with, or that I do not write to often, I will almost always start with the tried and true dear. This allows the person I am writing to the freedom to reply with the tone he or she prefers. If the relationship between us continues to be formal or impersonal (as in businesslike), I will continue the use of dear.
- not at all archaic (see any dictionary of contemporary English), and
- not a love-like salutation in most contexts, including business communication, and is
- by far the most commonly used salutation in both British and US English, in both formal and informal correspondence (wikipedia).
English may lack imagination when it comes to salutations; on the other hand, formal communication sticks with tried and true ways. For one thing, it aims to avoid miscommunication. Which is why dear is an old standard, still a standard, and likely to remain the standard for some time to come.
At some point, one or both of us may prefer a more informal tone. One can do this by using the person's name (with or without hello or hi, the latter being the most informal) in the first sentence of an email. After all, a person's name is the sweetest word to his or her ear.
Hello/Hi, Mary, I will send the files to you after I get back from the dentist's.
This approach avoids a separate line for the salutation, which keeps the email tidier.
For specific ways to address a chaplain, a reverend or a priest, you can do an internet search for clergy salutation. In most instances, it depends upon the denomination.
In other words, no, English does not have loads of synonyms for dear. This might be because written greetings, much like spoken ones, are quasi-ritualistic: How are you? Fine. And how are you? There are more differences in spoken greetings, but they often depend on the social distance and power relationship between the two people speaking, two criteria that will also factor in to how one greets another in a letter or an email.