Angels can be encountered without our realising

Hebrews 13:2 Do not forget to show hospitality to strangers, for by so doing some people have shown hospitality to angels without knowing it.

This is clearly a reference back to Abraham and Lot back in Genesis 18 and 19 and is intended to encourage hospitality. However, it does suggest that it is possible to meet an angel and not know, for them to appear incognito. Perhaps the idea is of the stranger brining the angels with him.

Angels rejoice when sinners repent

In Luke 15:10 it says that

... there is rejoicing in the presence of the angels of God over one sinner who repents.

If that is read carefully, it must mean thhat God rejooices when sinners repent. Undoubtedly the angels rejoice too.

Angels can be elect or non-elect

1 Timothy 5:21 I charge you, in the sight of God and Christ Jesus and the elect angels, to keep these instructions without partiality, and to do nothing out of favouritism.

Paul refers to elect angels, implying that there are also non-elect angels. Calvin says (Institutes 3.23.4) "The angels who have persevered in their upright state are called "elect" by Paul (1 Tim 5:21); if their steadfastness was grounded in the good pleasure of God, then the apostasy of the other angels shows these were forsaken. For that no other cause can be adduced than reprobation, which is hidden in God's secret counsel." This election must have been supralapsarian (logically before the fall) according to Geerhardus Vos. He suggests this election must be in Christ and in Christ as ruler and head (not Mediator). The elect angels did not fall but the non-elect did, according to the will and purpose of God.

Angels good and bad; some lost their positions of authority, some did not

Jude 1:6 And the angels who did not keep their positions of authority but abandoned their proper dwelling - these he has kept in darkness, bound with everlasting chains for judgment on the great Day.

2 Peter 2:4 For if God did not spare angels when they sinned, but sent them to hell, putting them in chains of darkness to be held for judgment; 

Some angels are good and some are bad, the demons or devils. They are described here as those who sinned and so did not keep their positions of authority but abandoned their proper dwelling (heaven?) and were sent to hell. God has kept them in darkness, bound with everlasting chains for judgment on the great Day. They may seem unchained but they are not really. When were they actually hurled down to hell? Probably when Christ died on the cross.

Angels are not to be believed if they say what is false

Galatians 1:8 But even if we or an angel from heaven should preach a gospel other than the one we preached to you, let them be under God's curse!

Paul is no doubt speaking of a hypothetical situation, although there is every reason to suppose a fallen angel preaching a gospel other than the one ... preached to the Galatians by Paul. As glorious and wonderful as angels are they are only to be listened to as far as they speak God's word.

Angels have a special commission to guard believers

Psalm 91:11, 12  For he will command his angels concerning you to guard you in all your ways; they will lift you up in their hands, so that you will not strike your foot against a stone.

These are the verses that Satan tried to misuse when he tempted Jesus in the wilderness. We are not to tempt God but we are to be confident that his angels will guard us in all our ways, if we are believers. They will make sure we come to no harm.

Spurgeon says that rather than having "one guardian angel, as some fondly dream" all the angels are active on our behalf. He calls them "the bodyguard of the princes of the blood imperial of heaven".

"It is down in the marching orders of the hosts of heaven that they take special note of the people who dwell in God. It is not to be wondered at that the servants are bidden to be careful of the comfort of their Master's guests; and we may be quite sure that when they are specially charged by the Lord himself they will carefully discharge the duty imposed upon them."

"The protection here promised is exceeding broad as to place, for it refers to all our ways, and what do we wish for more? How angels thus keep us we cannot tell. Whether they repel demons, counteract spiritual plots, or even ward off the subtler physical forces of disease, we do not know. Perhaps we shall one day stand amazed at the multiplied services which the unseen bands have rendered to us."

"as nurses carry little children, with careful love, so shall those glorious spirits upbear each individual believer ... even minor ills they ward off. It is most desirable that we should not stumble, but as the way is rough, it is most gracious on the Lord's part to send his servants to bear us up above the loose pebbles. If we cannot have the way smoothed it answers every purpose if we have angels to bear us up in their hands. Since the greatest ills may arise out of little accidents, it shews the wisdom of the Lord that from the smaller evils we are protected."

Angels are humbly slow to assert their own authority

Jude 1:9 But even the archangel Michael, when he was disputing with the devil about the body of Moses, did not himself dare to condemn him for slander but said, "The Lord rebuke you!" 

2 Peter 2:11  yet even angels, although they are stronger and more powerful, do not heap abuse on such beings when bringing judgment on them from the Lord. 

The allusion is an obscure one but the point is clear. Even Michael the Archangel, the head of all angels, did not take it upon himself to rebuke Satan or condemn his slander but meekly said "The Lord rebuke you!" . All the angels show the same modesty. In many cases they are stronger and more powerful then the fallen angels who oppose them but they do not heap abuse on such beings even when bringing judgment on them from the Lord.