After boiling pellets how can I deal with them? Is there a simple way to get them out of the wort, or can I leave them during fermentation? In that case will I be sure they will drop on the bottom and not cause problems?
Usually the pellets will dissolve during boil and settle down to the bottom of your kettle when you cool your wort. Then, when transferring to the fermentor you can just leave them behind (easier to do with a siphon).
Use a hop bag - put the pellets on the bag, when you are done with the boil simply pull the bag out.
I use a bucket for my fermentor so I bought a steel mesh strainer. I then sanitize the strainer with starsan and place the strainer across the top of the bucket and run the wort through it. This strains out the hop gunk and helps with aeration by turning the wort into droplets as it falls into the fermentor.
If you are siphoning your beer out of a flat bottom kettle/pot a whirlpool can be very effective.
After you are done chilling put your brew pot in the location that you plan to siphon from. Using a clean and sanitized spoon stir that wort up into a good vortex. Once the whirlpool has started, remove the spoon and replace the lid.
Then go about cleaning up from your session. Sanitize your fermentor and siphon equipment, prepare your yeast. If you give the pot 30 minutes at least to settle down much of the break material and pellet hops will get pulled to the center bottom of the pot.
Then you can remove the lid and siphon from the side of the pot without pulling too much of the gunk. Some won't hurt, but doing it this way will help you get much less of it if you want.
We filter the trub out through a sanitized fine mesh bag during siphoning. This way we don't worry about about the siphon pulling the trub - it ends up in what we call a trub sack, from which more wort is squeezed out while pulling it out of the fermenter. Make sure not to drop the bag into the fermenter, as trub sack may get heavy during the siphon. Not sure if there are any downsides to this method, we find it easy and seems to do the job.
This is what it looks like:
You can make a easy pellet strainer bag with cheap parts from a hardware store. This link offers easy instructions. Instead of one large dowel rod, one can use thread steel rods with washers and nuts in a plus shape to position in on a kettle and not slip.
I use a sanitized nylon bag, like the boil in bags. I bought it to replace the bag I use for mashing and filtering through my zapzap. It was too narrow for my kettle, so I re-purposed it as a hop filter after boiling. I sanitize by immersing it in boiling/boiled water for about ten minutes. I use my boiling spoon to help push out the retained liquids. I use buckets so the slightly smaller boil bag is perfect size. I like milancurcic's carboy solution, the narrow carboy neck acts as the system to push out the hops.