You are correct in your 3 points about the Cleric spells. Cleric and Paladin share the same method of 'Preparing' spells. Unlike most of the other Spellcasting classes; who choose spells as they level, the Cleric and Paladin simply know all of their spells of a given spell level. This is mitigated by the fact that they can only prepare so many of that extensive list per Cleric, or 1/2 Paladin level, and even farther by the consuming of spell slots to cast each of those spells.
I would give you reference pages for the PHB (Players Handbook), but if you're using just the basic guide that came with Starter Kit Adventure, you may not have access to it. Since I am running a cleric NPC, who is taking the Tempest Domain specialty, I'll use him as an example. The following is just to benefit anyone who may be having difficulties understanding the Starter Kit Cleric. This is an example of a fully realized Cleric from the supporting rules of the PHB.
Cleric is level 2 , and his Wisdom score is 16, giving him a +3 score. Clerics can prepare a number of spells = their Wisdom mod (3) + Cleric level (2) giving him the ability to prepare 5 spells total. There is a whopping 15 1st Level Cleric spells, and he knows them all! (I guess all those Cleric studies paid off...) He can prepare any 5 of those 15 spells during a Long Rest and switch them out with others on that same list every time he rests, keeping them in the forefront of his mind for casting purposes. Plus, as a Tempest Domain Cleric, he gains two additional 1st Level spells that are permanently prepared, bringing him up to 7 prepared spells total. As a Level 2 Cleric, he has 3 1st level spell slots. Of those 7 prepared spells (5 that you choose and can switch out as needed during Rests, 2 that are locked in place permanently), you only have 3 slots to burn on them, in any combination of spells you choose. Casting a spell requires spell slots and does not remove it from your prepared list, meaning you can cast it again so long as you have slots remaining. It allows the Clerics and Paladins a measure of diversity and strategy in adapting to situations.