It might be better if you just explained what it is you need to do.
There are many types of mixing console around for "specialized" purposes, but, this does not mean all of them are cheap or "specialize" in the way you might want them to.
Question 1 - This is usually want the Insert is for. The input of the channel strip is sent to the insert out, you can run that to whatever you want, the output of the component hooked up the insert out will output to the insert in, then it will continue to the rest of the channel strip.
Some mixers have a Direct Out on every channel strip. On less expensive consoles, this Direct Out is Post Fader, so if you were using the insert on the channel, that would be before the Direct Out, so anything present on the insert chain will be present at the Direct Out.
There are some mixers with "In-line" monitoring which would allow you to have two inputs present in the same "strip" of the console, but, there are no consoles that I know of that off have idividual Aux outputs per channel. That would add up to A LOT of outputs on the console, which is why the master Aux output is used for Aux sends.
Question 2 - There may be, but this would be a VERY unusual setup in either case. Think of your mixing board as your nerve center of the studio. Most recording consoles are well laid out for it's task. There ARE mixing consoles that have Sub Group ouputs, and this can range from 2-24 Group Outs, but usually the more group outs you have, the more expensive the console it. I am sure too that there are many cheap mixers that don't have Auxillary outputs at all and just eq.
Again, maybe you should explain what it is you are trying to do. I have a feeling that your needs would be simple to fulfill, you just may not be aware of how it is properly done with equipment that is currently available.
Ed