To point 1
Does slipping mean zero angular velocity or is it just the v velocity not being equal to wr?
The geometric bond $v=\omega r$ tells the speed $v$ of a particle a distance $r$ from the wheel centre. Within the wheel, this equation must hold true for every particle - otherwise the wheel would break apart because particles would "skew" relative to each other.
A particle on the rim, the periphery, must also obey this equation. At the contact point with the ground, the ground particle should follow this rim particle and should thus also follow this equation in order to not "skew" and move differently relative to the rim particle. If the ground particle does not fullfil this equation, then you have sliding.
The speed of such ground particle (the speed of the ground) is relative to the centre of the wheel (rotational centre or centre-of-mass). This is equivalent to the speed of the centre-of-mass (so the linear speed of the wheel as a whole) relative to the ground.
So, sliding and slipping for a wheel means that the the centre-of-mass' speed, $v\neq \omega r$ is not fulfilled. But $\omega$ does not have to be zero - the wheel can rotate just fine regardless of whether it matches the motion relative to the grond (think a spinning ball on ice).
To points 2 and 3
Without friction there is no (tangential) tie between wheel and ground. There is thus no reason to expect the equation - the geometric bond - to be fulfilled.
So, when rolling up an incline, the wheel will ideally continue spinning even as it slows down linearly - and it will continue spinning as before even while speeding up downwards.
With friction we would expect the ground to "grap onto" the rim and keep the geometric bond fulfilled, as long as the friction is strong enough.
To point 4
Can I use conservation of angular momentum when friction is present?
The angular momentum conservation law always holds true. Whether you can use it only depends on whether your system is not too complicated to calculate for. Whith friction slowing down the wheel rotation, angular momentum conservation tells us that the Earth obtains some oppositely directed angular momentum. This is obviously easily lost as insignificant, and so this law might rarely be useful in such case.
But it depends on what you need to find with this law. Maybe friction isn't relevant for a particular scenario. So this question is too broad to be answered generally.