You are able to cast the cleric spells at a higher level.
While spells known / prepared are handled on a class basis, your spell slots are combined.
PHB, page 164, Multiclassing, Spellcasting, Spell slots
Spell Slots. You determine your available spell slots
by adding together all your levels ... Use this total to determine your spell slots by consulting the Multiclass Spellcaster table.
Regarding your ability to use the cleric spells in these slots, a few sentences later it says
If a lower-level spell that you cast, like burning hands, has an
enhanced effect when cast using a higher-level slot, you
can use the enhanced effect.
Consult the multiclass spell slot table on the next page, and those are your slots. You can use any of the spells you have prepared, from either class, in any of those slots.
So, for example, as Sorcerer 19 / Cleric 1 you could cast Cure Wounds in your sole 9th level spot, healing for 9d8 + Wis, but then you would no longer be able to use that slot for sorcerer spells.
Yes.
From the Hypertext d20 SRD:
Divine spellcasters prepare their spells in largely the same manner as wizards do, but with a few differences. […]
Spell Selection and Preparation
A divine spellcaster selects and prepares spells ahead of time through prayer and meditation at a particular time of day. The time required to prepare spells is the same as it is for a wizard (1 hour), as is the requirement for a relatively peaceful environment. A divine spellcaster does not have to prepare all his spells at once. However, the character’s mind is considered fresh only during his or her first daily spell preparation, so a divine spellcaster cannot fill a slot that is empty because he or she has cast a spell or abandoned a previously prepared spell.
From d20PFSRD:
Spell Selection and Preparation
A divine spellcaster selects and prepares spells ahead of time through prayer and meditation at a particular time of day. The time required to prepare spells is the same as it is for a wizard (1 hour), as is the requirement for a relatively peaceful environment. When preparing spells for the day, a divine spellcaster can leave some of her spell slots open. Later during that day, she can repeat the preparation process as often as she likes. During these extra sessions of preparation, she can fill these unused spell slots. She cannot, however, abandon a previously prepared spell to replace it with another one or fill a slot that is empty because she has cast a spell in the meantime. Like the first session of the day, this preparation takes at least 15 minutes, and it takes longer if she prepares more than one-quarter of his spells.
(emphasis added to both quotes)
The "particular time of day" clause limits them only as far as the first daily spell preparation, i.e., the one in which they regain spell slots.
Best Answer
Each day, you can prepare a total number of spells as listed in the table, plus any bonus spells you get for a high Wisdom score.
For example, a 1st-level cleric with 18 Wisdom: the table says 1+1 first-level spell slots, which is to say 1 from the cleric list and 1 from one of his domains. He also gets a bonus first-level slot from his high Wisdom. So, ignoring his domain spell slot, he can prepare two spells that day.
That means he can prepare, for example, 1 use each of divine favor and magic weapon. Or he could prepare 2 uses of divine favor, or 2 uses of magic weapon. And the next day, it’s the same deal but could be any cleric spell or pair of cleric spells. But he has to choose how many of each to prepare each day.