“mix with.” Literally “come into.” In some contexts, “come into” is idiomatic for sexual intercourse, but that may be going too far in this context (cp. Josh. 23:12, which uses the same phrase).
“nor serve them.” This refers to the work of worship.
“bow down.” The common biblical way of bowing down before people or God was to fall to one’s knees and bow the upper body to the earth. It is the same Hebrew word as “worship.”
[For more on bowing down, see commentary on 1 Chron. 29:20.]