....a little patience..... forums are not immediate and you should know this.
what is the purpose of the headphones?
if you will be listening to only music then a dac+amp would be good. however, if you want to be gaming you may want to consider a soundcard instead for virtual surround. if you do not care for virtual surround then by all means you can use a dac+amp instead.
the e10k is the newer version of the e10. the older e10 had a slightly warmer sound with more bass boost while the new e10k is more neutral with just a slight hint of bass boost and warmness. otherwise, they are similar.
yes, you can use it with your dt990-250.
if you wanted a soundcard, you can get a creative z for $80 which will power them just as well and give you virtual surround as well which is also good value for the money spent.