[RPG] How many spells would a 1st-level Wizard be able to prepare per day

Yes you get to learn all those spells you mentioned, but magic always comes at a price. In this case while you "know" a bunch of spells you can still only cast a specific number of them each day. So at level 2 you can cast your at-wills 1 encounter, 1 utility and 1 daily spell (not including cantrips and rituals). You just get to choose which one you will, for lack of a better term, "charge up" for the day. Like Peteris said, at each extended rest you must choose which of your spells you will prepare for the following in game day. This keeps you at the same power level as other same level characters (except you get +1 at will that you can use at any time).

So, Bob the level 2 wizard opens his spell book in the morning after getting a good night sleep and turns to his "Utility Spells" page. He sees Expeditious Retreat and Shield, not wanting to get too close to enemies, he chooses to memorize the evasive spell Expeditious Retreat absorbing the spells magic for use later that day. He then flips through his spell book and does the same thing for the daily spells he has in his book. He then sets off on his travels with his companions being able to cast 3 at wills, 1 encounter, 1 utility and 1 daily.

The benefit here is if you know you'll be facing a certain creature and you have a spell that will deal lots of damage to it, you can prepare specifically for that engagement.

Can I use bonus slots to cast spells above what my class level normally allows?

No.

According to the official Paizo FAQ, you can only use bonus slots for spell levels that your class and level has access to.

For an example of this in action, the Paladin has a "0" in his Level 1 spells per day entry at level 4 (note that up to level 3, he has a "--"). This means he is granted 0 level 1 spells but can use his bonus slots, if he has any, to cast level 1 spells. As far as I am aware, only the ranger and paladin classes fall under this scenario, where bonus slots might grant casting before a class feature gives any per day spell slots.

Copying A Scroll into a Spellbook

There are no restrictions on spell level aside from the usual checks required to copy a spell into the spellbook. The wizard deciphers the magical writing on the scroll and once he has done so, he studies the spell for a minimum of one hour. At the end of the hour he makes a spellcraft check (DC 15 + spell level). If the check is successful, the spell is copied into the book regardless of the level. Copying the spell into the spellbook also costs GP based on the spell level; the exact costs are found in the table under the header Writing a New Spell into a Spellbook on the PRD page for Magic. If the spellcraft check fails he can't try again until a week has passed; the scroll is not consumed.