church (v.1) = Lit. “a company called out” — the Greek word is used in Scripture to refer to the Israelites (Acts 7:38); an unruly mob (Acts 19:32); an assembly of governing citizens (Acts 19:39); all those saved in the current dispensation into the Body of Christ (Ephesians 1:22-23); all those saved in the prophetic kingdom (Matthew 16:18); or a local assembly of believers, as here
Lord (v.1, 2x) = master, owner — a title of respect — Jesus Christ used the title to describe Himself (John 13:13).
grace to you and peace (v.1) — the latter was the usual greeting among the Jews (cp.Matthew 10:12-13; Luke 10:5), as chairete – “rejoice!” was among Greeks (Acts 15:23). This latter, however, the apostle Paul does not use, but for it substitutes charis = grace. — Vine, page 19.
always (v.2) = on all occasions
without ceasing (v.3) — the same word is used in secular writings to describe an incessant cough, so Paul isn’t talking about uninterrupted prayer but constantly recurring prayer.
work of faith (v.3) — Paul describes this in 1 Thessalonians 1:9: … you turned to God from idols … — The same idea is found in John 6:28-29: Then they said to Him, “What shall we do, that we may work the works of God?” Jesus answered and said to them, “This is the work of God, that you believe in Him whom He sent”.
labor of love (v.3) — Paul also describes this in 1 Thessalonians 1:9: … to serve the living and true God. Labor, here, is “toil resulting in weariness”
patience of hope (v.3) = patient endurance (under trial) while waiting for Christ’s return — That the Thessalonians had been doing this can be see in 1 Thessalonians 1:6; 2:14 — In 1 Thessalonians 1:10, the patience of hope is described as … to wait for His Son from heaven … — Hope, here and most places where Paul uses the term, refers to faith in the future, confidence that God will do what He promises.
in (v.3) = should be “of” (patience of hope of our Lord Jesus Christ)