As someone who builds multiclass almost any time it is allowed, I have been over this a lot and, unfortunately for us multiclassers, this is a case of a rule trumping/replacing another rule, not combining rules. The confusion arises from this important distiction being forgotten because it's easy to misread what is trumped and what is combined, which I'll get into presently.
The 'Classes' section and coresponding write ups of each class assume you are Single Classing. If you are multiclassing, some rules are different for you. The section on Multi Classing details How the rules for you are different than single class characters for spellcasters, this includes how you determine what spells you know and prepare and what spell slots are available to you. Instead of the rules in the 'classes' section, you use the rules in the 'Multi classing' section just like you do for skill and saving throw proficiency. The problem arises because the multiclass rules for spells known ask you to reference the 'classes' section but with an important caveat. It does look, at first glance, like you could prepare/learn spells of your highest multi class slot level, using the rules from 'Classes' but the multi class section, before directing you there, states you determine spells known/prepared based on your individual levels in a given class.
So, a wizard 3/Cleric 10, when referencing the wizard rules to determine what sweet wizard spells they have access to, must remember they can learn/prepare only those spells available to 3rd level wizards even if they have 10 levels of cleric as well. The spellbook and spells at higher level blurbs do state that they can learn/prepare any spell for which they have slots available (in this case 7th), but the multi class rules, which trump single class rules in this instance, state they calculate what wizard spells they can Learn/Prepare as if they were a 3rd level wizard only (in this case 2nd level spells max) and their cleric spell access as if they were a 10th level cleric only (in this case 5th level spells max).
Their spell slots available are the only time they combine caster levels, which is why the rule looks fuzzy because if i have 6th level spell slots, why can't I prepare disintegrate? because you determine wizard spells known/prepared as a 3rd level wizard, who would not have 6th level slots. They need to post an errata or something to make this clearer, that's all
I mention all this because the 2nd question has been a subject of debate a lot.
Taking this into account
Question 1) Yes 100%. Total spell slots available for whatever spells you know are determined by combining spellcasting levels, what spells you have access to are determined individually.
2) Yes but spells available are determined by Cleric level and what slots a cleric of that level would have, not the max slots you as a multiclass cleric/bard have. Same goes for what bard spells you know.
3) Yes each spell you know and prepare is associated with one
of your classes (Bard or Cleric for you), and you use the spellcasting ability of that class when you cast the spell. Similarly, a spellcasting
focus, such as a holy symbol, can be used only for the
spells from the class associated with that focus.