basically there are pros and cons to having a filter on your lens.
let me sum up the pros 1st:
1) filters are your 1st line of protection from any knocks, smudges, dust and dirts. meaning in case any thing happens, you just change your filter, not you lens. imagine spending a few thousand on a good lens then you land a scratch on it...?
2) there are also different filters to achieve certain effects you need. for example UV filter is mainly for protection, CPL filter is ensure light enters in 1 direction hence giving you a "bluer" sky and also prevent reflection. while a ND or GND filter gives you the extra stops you will need for you filter.
next on to the cons:
1) filters of normal quality some times degrades the image quality. however this is only visible when you pixel peep.
2) if you use filters on a UWA lens, it might show up on your picture...
so, if you do not know if you should get a filter or not, my suggestion to you is that you get a norm cheap filter on every of your lens. it''s for protective purposes more than any thing else...
You do not leave the CPL on your lens all the time. You only use it when you need it.
For adding contrast and removing haze, CPL works best when the sun is perpendicular to the direction where your lens is pointing. So this means if you are shooting into or away from the sunset/sunrise, a CPL is not very useful in giving you more contrast.
You will lose light when using a CPL. Depending on the specific model and brand, you will lose around a 1 to 1.5 (even 2) stops of light. You can use this to your advantage if you know how.
You use a lens hood to keep stray light from entering your lens to prevent lens flare.
They do different things. Can't tell you which is better. You need to decide at that point in time, what you need for the particular scene you are shooting.