This phrase is an idiom that means "come into my house." If your language has an idiom that means "come into my house," think about whether it would be good to use here. (See: [[rc://en/ta/man/translate/figs-idiom]])
The servant understood that Jesus could heal the servant just by speaking. Here "word" refers to a command. AT: "just give the order" (See: [[rc://en/ta/man/translate/figs-synecdoche]])
# my servant will be healed
The word that is translated here as "servant" is normally translated as "boy." It may indicate that the servant was very young or show the centurion's affection for him.