It's my first time using paint rollers, and I have a problem. How do I store a paint roller cover for 2 hours so that I can use it for a second coat?
Wrap the roller in aluminium foil. Or in cling film. I've stored rollers this way for 2 weeks, though you do risk it getting a bit dry and crusty at the edges for that sort of longer period. For 2 hours you'll be fine.
The point of wrapping it is to stop air getting to (or getting away from) the paint that's on the roller. Solvent paint (i.e. most paint) dries by evaporating the solvent into the air - if there's no air it can't easily evaporate.
(If you're in the US, feel free to use aluminum foil or saran wrap instead...)
I simply load the roller (to keep it moist), lay it in my tray, along with the brush, and wrap it with a kitchen trash bag. Squeeze most of the air out.
This works well for 24-48 hours. Longer than that and you'll start to get drying on the edges of the roller and the brush. Tools should be cleaned for longer storage.
I have stored rollers for many days by taking a shop towel or paper towel and getting it wet, i ring it out so it is damp and not dripping. I then spread it out flat, take the roller and place it on the edge of the towel and roll the roller so that the towel rolls up around it. I then roll that up in plastic or place in a Ziploc type bag. The damp towel allows it to keep longer than in just plastic alone.
I did pick up some wet roller zip type storage bags at a locally owned hardware store in the paint section that worked great, they are exactly the right size for a roller. I still use the damp towel for long term and to avoid the mess of fitting the roller into the narrow zipper opening. I do not know the brand name.
For latex paint (you fail to specify, but it's what's common) the supposedly quick & easy option is to wrap in plastic wrap, then seal in a bag, then put in the freezer.
I don't actually bother with that, as the standard cleanup is hardly any more difficult and does not involve finding freezer space for a non-food item. Wash the roller and pan with a hose until it seems basically clear, then wash with soap and warm water, then rinse throughly, and finally let dry (clean off all paint residue.) 2 hours, 2 days, 2 weeks or 2 years, this method works...
Oil-type-paints are more of a pain due to the solvent not being water.
Your second question should be a second question (i.e. delete from this one and ask it separately) but probably has most to do with "dipping paint roller in bucket of primer" rather than using a proper roller tray. Inexperienced painters often think they are saving time and trouble by painting right out of a can, rather than using a roller tray. This could not be further from the truth. The small loss of paint in cleaning the roller tray is trivial, and results are much improved when the roller is properly loaded. When dipping it in a bucket, you overload the roller, at least on the side you dip; if you dip the whole thing you also get paint where it should not be in the roller bearings & interior, and overload the whole thing. Too much paint on a roller causes it to slide like a wheel in mud, rather than rolling.