Can a wizard use spells from their spellbook without preparing them? Outside of combat as well?
Only if it is a ritual, and is cast as one
A wizard must prepare a list of spells they have available to cast. Available spells do not depend on being in or out of combat, but are simply the spells the wizard has at their disposal. A wizard could cast a cantrip without "preparing" it, but cantrips are not spells "from his [spell]book". The only way to cast a spell from your spellbook without preparing it is if it is a ritual (PHB, p. 114):
Ritual Casting 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.
So as long as you spend an extra 10 minutes casting your spell, and it has the "Ritual" tag, you do not need to have it prepared. Otherwise, you can only cast prepared spells.
Note: This question is tagged 5e and my previous experience with this houserule was in 2 and 3.5!
I've had it before where the spellbook could be treated as a sort of pseudo-scroll, in that you've written it down to be able to learn it with study every day, but you can cast it directly from the page with the side-effect being the spell text gets wiped from the book forcing you to find another scroll to learn it from.
The cost of losing the spell from the book made it a last-choice for using it (emergency teleport or similar) - but the choice did allow for changing how to take on situations, and also allowed for extra use out of found spellbooks with overlapping spells (the issue of using someone else's spellbook would be a different question).
This was a definite fudge, in that the spells are supposed to take up X pages, and clearing one out the middle would technically mean that writing a new spell in the space could split it into sections. We did run it that the words of the spell were burnt out, rather than the pages it was written on (so it was used on at least one occasion to quickly wipe a spell from the book to allow a different one to be written in its place).
With the 5e ritual tag affecting most of the relevant out of combat spells I've not considered adding it as a houserule since starting 5e
By rules no, just read Gandalfmeansme excellent answer to this.
That said, if you are a DM, than you can most certainly include this future for a Wizard. For most part this wouldn't be very damaging in terms of balance. That is because almost all combat spells would be largely useless if you made them a ritual spells (a fireball that takes 10 minutes or longer to cast isn't precisely very useful).
That said some spells, especially at higher levels would in fact be dangerous if you allow them to be cast many times in a day. Just think of a spell like True Polymorph. It is bad enough to have this spell cast once a day... but if you allow it to be cast every 10 minutes? WOW!
Even combat spells would be incredibly potent in a specific situations, such as for instance during a siege. Imagine being able to cast Earthquake every 10 minutes, what would that do to a rampart?
Therefore you should be very careful with how you would want to implement this, but it may make sense in your game.
To give you an idea, in my game there are cadres of Wizards who can combine to cast spells. This is clearly against the rules! But it works within the setting I have. However the secret of doing so is, just that a secret, and basically it is more of a NPC thing, for various story reasons.
I can see, allowing casting of spells from a spell book, but limit it. Perhaps after doing so, caster needs a rest? May be even a long rest! Or may be he has to make a Constitution saving throw of 10 + spell level. Failure of which does him spell level x d6 of damage and spell fails?
Something like that, to prevent this from being abused, but yet allowing it. Do keep in mind that this will make ritual spells less desirable, and special.