Naomi Novik's excellent recent novel Spinning Silver features a Jewish family working as moneylenders in a village with no other Jews. The nearest Jewish community is in a city a full day's ride away.
The setting is ambiguous (its a fantasy novel, so not literally set in any real time/place), but it's reasonable to guess it's Lithuania in 1708-9 during the Great Frost.
As a fantasy novel, I'm not expecting it to perfectly reflect the reality of Jewish practice in early 18c Lithuania, but I'm curious to the extent that it does.
Would standard Jewish practice in 1708 Lithuania require the head of this household to live near a minyan for daily or weekly prayers? Or was it unremarkable for Jews to live outside of Jewish communities for business purposes?
Novak's novel includes an intermarriage between a Jewish girl and a gentile, officiated by a rabbi but (seemingly) without the gentile converting to Judaism. How likely is it that such a marriage could have found a rabbi willing to officiate?
The short answer is yes- most Jewish families in Lithuania at that time would be living in a village (shtetl) or town, with access to a minyan and other amenities which come with living in a Jewish community. There could be backwater Jews who did not, but this was relatively uncommon, and it would be less because they were living in a non-Jewish town and more because they were living in the backwater somewhere as farmers (also uncommon). The exception would be when a Jew was the "court Jew"- not so much a moneylender as a banker or financier who was employed as the personal financial manager of a local ruler (often as the only Jew permitted in that area). Bear in mind that in these times, Jews were prohibited from living in many places, or restricted to certain areas- which could, just as much as Jewish law and community, be a reason for Jews to stay close together.
For the record, the trope of the Jew as the moneylender (as opposed to a banker/court Jew) is actually more of a medieval than an early modern one, so that itself rings a bit false, but it's not like it's impossible.
As far as the marriage, I cannot at all imagine a rabbi in that time and that place officiating at an intermarriage. This is not only due to the fact that Jewish law would have forbidden it (and that all rabbis at that time and in that place would have followed this law), but due to the fact that marriage was seen as entirely religious- it would be seen as just as problematic from the Christian side for a Christian to be married by a Jewish rabbi as it would be from the Jewish side, and it would be seen as no marriage. The concept of intermarriage at all was basically unheard of- one or the other would have to convert.