We present a survey of far-ultraviolet (FUV; 1150 - 1450 Ang) emission line spectra from 71 planet-hosting and 33 non-planet-hosting F, G, K, and M dwarfs with the goals of characterizing their range of FUV activity levels, calibrating the FUV activity level to the 90 - 360 Ang extreme-ultraviolet (EUV) stellar flux, and investigating the potential for FUV emission lines to probe star-planet interactions (SPIs). We build this emission line sample from a combination of new and archival observations with the Hubble Space Telescope-COS and -STIS instruments, targeting the chromospheric and transition region emission lines of Si III, N V, C II, and Si IV. We find that the exoplanet host stars, on average, display factors of 5 - 10 lower UV activity levels compared with the non-planet hosting sample; this is explained by a combination of observational and astrophysical biases in the selection of stars for radial-velocity planet searches. We demonstrate that UV activity-rotation relation in the full F - M star sample is characterized by a power-law decline (with index $alpha$ ~ -1.1), starting at rotation periods >~3.5 days. Using N V or Si IV spectra and a knowledge of the stars bolometric flux, we present a new analytic relationship to estimate the intrinsic stellar EUV irradiance in the 90 - 360 Ang band with an accuracy of roughly a factor of ~2. Finally, we study the correlation between SPI strength and UV activity in the context of a principal component analysis that controls for the sample biases. We find that SPIs are not a statistically significant contributor to the observed UV activity levels.
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