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.
Yes. You can cast any spell using a slot of the same level as the spell, or higher.
From PHB page 201, Chapter 10: Spellcasting:
SPELL SLOTS
[...]
When a character casts a spell, he or she expends
a slot of that spell's level or higher, effectively "filling"
a slot with the spell. [...]
and, later on the same page:
CASTING A SPELL AT A HIGHER LEVEL
When a spellcaster casts a spell using a slot that is of a
higher level than the spell, the spell assumes the higher
level for that casting. For instance, if Umara casts magic
missile using one of her 2nd-level slots, that magic
missile is 2nd level. Effectively, the spell expands to fill
the slot it is put into.
Some spells, such as magic missile and cure wounds, have more powerful effects when cast at a higher level, as detailed in a spell's description.
Note: In your example, you had both 3rd and 4th level spells slots remaining. You can cast Shield with either a 3rd or 4th level slot but (as there is no enhanced effect for that spell when cast at higher levels - a Shield spell is a Shield spell no matter what level it's cast at), it would be best to cast it as third level spell - keeping the 4th level slot for future 4th-or-lower level spells. Shield doesn't benefit from higher slot levels, but some other level 1-3 spells you might want to cast do.
In other words, cast it with the lowest level slot that will achieve the desired effect, taking into account any possible enhancements from casting at higher slot levels
For example, as mentioned by Mark Cogan, when casting Dispel Magic or Counterspell at higher levels, each increase in slot level increases the level of spell which can be automatically dispelled/interrupted without a spellcasting ability roll.
Similarly, Fireball can be cast using any slot of level 3 or higher - but you don't need to use a 9th level slot against a bunch of kobolds unless you have no lower-level slots remaining.
Best Answer
This works.
A fireball cast at 4th level is properly a 4th level spell. The rules for 'Casting a Spell at a Higher Level' say:
The fireball is 4th level, so you can replace the fire damage with psychic damage if phantasmal killer appears in your spell book. It does not have to be prepared.