[RPG] How to determine feats for a new character

Feats are based on character level, not class level

All characters gain a feat at first level, then another every two levels thereafter. This is based on your character level - that is, the sum total of all of your class levels. Your feat breakdown should look like this -

Human Cleric 1 (ECL 1) - 2 feats at first level (2 feats total)

Human Cleric 2 (ECL 2) - No additional feat

Human Cleric 3 (ECL 3) - 1 additional feat (3 feats total)

Human Cleric 3/Fighter 1 (ECL 4) - 1 additional feat (fighter bonus feat, 4 feats total).

Fighter's bonus feat is its class feature and is unrelated to the feats gained through your ECL (Equivalent Character Level).

As far as feats go, Combat Reflexes and Improved Initiative, from your list, are both solid. Power Attack may not be a good choice; your attack bonus will be low for your level and Power Attack may just remove any chance you had at hitting. Channel isn't really the greatest ability to invest in and you might want to consider some metamagic feats instead, as a down-the-road investment.

This is not a typo or mistake.

While WOTC may not have the best track record for publishing without errors and their length errata for all editions they've ever published exists, its not a safe assumption to presume that this was an error.

Neither the Ranger nor someone with the Initiate Feat should get one....

The Ranger doesn't receive spells until level 3 and the types of spells the Ranger gets are generally used as utility spells. They buff the party, the ranger, or trigger against an enemy without a DC roll. Its not as important that a Ranger has a spell focus because their main way of dealing damage is not spells but their class features combined with a longbow.

As far as initiate's go, your getting 2 cantrips and only 1 spell. The character is at best a dabbler. If they already have a focus as part of their main class (or multiclass) than yes they could use it for their spells, but they are already experts at magic. A barbarian that takes a Initiate feat should be notably not as good at it as someone who is trained.

As you noted characters can simply multiclass instead to gain better casting. That is the whole point of multiclassing, getting access to full class features. The opportunity cost is that by multiclassing you delay your main class level up and deny yourself a capstone feature.

In summary:

1. No

2. Yes