Warhammer 40k Unit Composition - Marines
Yes, its perfectly fine to play your custom chapter as ultramarines. The fluff says that most chapters follow their example.

As for using special characters, yes you can use them in a non-space marine army. An FAQ in White Dwarf answered a similar question for blood angels:

Q: Can I use Commander Dante [commander of the Blood Angels chapter] as my Flesh Tearers chapter leader?
A: Yes, but keep in mind that he is the Blood Angels chapter leader, not the Flesh Tearers.

Hope that helps.