A question about filters and my "new" lens...

[Phil]

Hi,
As some may know, I've been attempting photos of stars...
I decided the best thing to do would be to buy a wide angle lens. I saw a Sigma 10-20mm f4 lens for a good price and bought it.
I know its not especially fast, but I have to work to a budget.
It turned up and was immaculate. It had also been fitted with a filter of the brand "camlink."

Now I've noticed two things.

First up, the lens. When taking regular photos in daylight, I have to have a very low shutter speed, when compared with my other lenses. Is this normal with a wide angle lens?

Second question which is specific to the filter.
Last weekend I went out at night and the front of the lens misted up over the filter. This has never happened for me before. (I usually use Hoya or Gobe filters.)

So do cheap filters (camlink) tend to mist up easily? Do better quality filters have some anti fog coating??