παῖς [2 verses](noun sg /masc/fem nom) "Servant" is pais, which means in relations to age,  "child" of either sex, and, in relation to condition, "slave" or "servant."  - Though translated as "servant," this word more likely means "child." Jesus clearly uses it to mean "child" when addressing a young girl and the other times it is used in the gospels, it could mean "child" as well.

πάλαι [2 verses](adv) "Long ago" is from palai, which means "long ago," "long ," " of old," "before," "just past," and similar ideas. With present, means something lasting to the present. With past, something lasting to the past.  -  "Long ago" is an adverb means "long ago," "long ," " of old," "before," "just past," and similar ideas.

παλαιούμενα,[1 verse](part pl pres mp neut acc) "Wax" is palaioo, which means "decay through time", "make old", and, of wine, "become old". - - The verb translated as "wax"  means to "decay through time", "make old", and, of wine, "become old". It is the form of an adjective, "decaying". 

παλαιούς: [8 verses](adj pl masc acc) "Old" is palaios, which means "old in years," "ancient," (in a good sense) "venerable," "held in esteem," (in a bad way) "antiquated," "obsolete," and "in an old way." -- The word translated as "old" means old in years both in a good sense and a bad one. In a good sense, it means "venerable" and in a bad sense, "obsolete."

παλινγενεσίᾳ, [1 verse](noun sg fem dat) "Regeneration" is paliggenesia, which means "rebirth," "regeneration," "beginning of a new life," "restoration (of world)," and "reincarnation (of a person)."  - "Regeneration" is from a noun that means "rebirth," "regeneration," "beginning of a new life," "restoration," and "reincarnation." The can mean anything from the reincarnation of a person to the rebirth of an age or world.