If you have really, really, good water quality and your tank is established you could probably handle an anemone.
As far as a skimmer, my personally recommendation for a 10 gallon nano is a Skilter 250. It is a combination skimmer/filter. They don't do much for larger tanks but IMO are great for nanos. I have a Skilter 500 on my 20. I love it, however some have had problems, especially on larger tanks.