Part 1: When selichos are said on a “minor” fast day such as shiva asar b’tammuz, is tachanun said as part of selichos, or is that only on asseres yemei teshuvah?
Part 2: When tachanun IS said as part of selichos, then if there is a bris in shul on that day is tachanun in selichos skipped?
Generally tachanun is said after selichos on a fast day.
On fast days when there is a bris, selichos are said, but tachanun, meaning Vhu Rachum [on Monday or Thursday] and Nefilas Apayim [on all days] are omitted.
See Shulchan Aruch Y:D 265:13.