This is one of those changes from 3.5e to 5e D&D
There was a mechanic in D&D 3.5e wherein a Wizard or other spellcaster that uses the spell preparation mechanic could in essence leave a few of their spell slots unprepared so that later they could be filled as necessary with spells that they might need throughout the day. These "late preparations" took a minimum of 15 minutes but allowed the spellcaster to get a deal of utility out of spells that had a non-combat role. The caveat was that the slots had to be empty and you couldn't drop a slot you had prepared a spell in to prepare a new spell unless you had just finished a full rest period.
The new edition introduced ritual spells to cover some of the need for this
Preparation in 5th edition changed a great deal from prior editions of Dungeons and Dragons. The 15 minute spell prep by leaving spell slots empty isn't really required anymore due to the ritual mechanic which allows using 10 minutes to cast non-combat spells (that have the ritual tag) outside of combat. This provides the Wizard with a lot more versatility on how to choose the spells they'll use to deal with the challenges they believe they'll face that day. (Gonna be in the middle of the desert? Probably won't need feather fall.)
The 5e rules also opened up your spell list so that you can prepare less of one spell level and more of another, giving many choices on how many spells of each level you'd like to prepare. You are no longer locked into 4 first level spells and 2 second level spells. You could choose to prepare 2 first level spells and 4 second level spells so you have more of the useful spells available to account for your daily challenges and to get the most out of your higher level spell castings.
What is your DM's preference?
Fifth edition never states that you can't prepare five of your six daily spells and leave the six slot open to prepare it later as you may need it. It also doesn't explicitly say that you can do that either. It's a decision that will most certainly have to be made by your GM. For instances where the book doesn't explicitly state what you can and can't do, the GM is responsible for making a call that might or might not allow you to do that thing.
Is it needed?
The usefulness of this is actually a great deal less than in 3.5. Due to the availability of ritual spells and the greater flexibility in spell preparation, there is less of a need for leaving empty slots in 5e than there ever has been in D&D. In short, the introduction of ritual spellcasting has removed the need for an empty slot / late preparation requirement that just wasn't present in prior editions of Dungeons and Dragons.
Each caster class is treated a bit differently.
Check the PHB for specifics for each class to understand how the ritual tag applies.
Ritual Casting (Wizard) Basic Rules p. 30
You can cast a wizard spell as a ritual if that spell has the ritual tag and you have the spell in your spellbook. You don’t need to have the spell prepared.
The Cleric doesn't get the same benefit, for example.
Ritual Casting(Cleric) Basic Rules p. 22 You can cast a cleric spell
as a ritual if that spell has the ritual tag and you have the spell
prepared.
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
My understanding is that druids do get to pull from their entire pool of spells. Druid spells tend to be lower impact than wizards, reducing the harm.