"I like the monarch lathe but I really like the 10EE but they only have 20" CC."
A 10 x 30 model (12.5 x 30 actual) was offered, but it is exceptionally rare.
It is also exceptionally expensive.
A 13EE or an EE1000 is perhaps more common than a 10 x 30, but these models are generally found in so-called National Labs (Los Alamos, Hanford, Oak Ridge, etcetera, the "usual suspect" nuclear weapon labs). A 13EE/EE1000 is a 13 x 54 machine (15.5 x 54 actual) and may be the most expensive toolroom-type lathe ever made. These are certainly the most complicated.
"how who you do barrels that were longer that would not be a pain in the pants getting it set up"
You need an engine lathe with a contouring capability, not a pure toolroom lathe such as an EE.
Toolroom lathes are intended for making tools, not for production, although during WW-II 10EEs were certainly used in a production capacity, making all kinds of super-precision parts on a 24/7/365 basis.
"I have some having me take notice of the 10EE along with other, I really like them [ but ] I am not a full time machine and have to find method and ways to do some types of work"
A 10EE is not intended for this kind of work.
Rather, a 10EE is intended for tool-making or for production of parts to exceptionally tight tolerances which are within the scope of the machines (10 x 20 or 10 x 30). Also, the "through hole" capacity of a 10EE (either model) is relatively small, in order to maintain the maximum possible rigidity of the spindle. Gunsmithing and similar trades require a through hole capacity which significantly exceeds that provided by an EE.
For longer parts, a "x 54" lathe is certainly preferred as this can accommodate most barrels while turning between centers (see, for example, Grizzly's so-called "gunsmith lathes").
"can a longer barrel be done with ease using a 10EE?"
The machine was not intended for relatively long, relatively thin workpieces.
"I have seen collet closer and other parts for using 5C"
Sure, the 10EE has a 5C nosepiece and either a drawtube or lever closer.
But, so also do most lathes which have a 5MT spindle.
The 10EE has a Jarno taper, which is standard for Monarch, but may be unusual for competitive lathes.
"and could someone please tell what is meant that it has taper attachment"
In the Monarch context, it is a patented device which allows the setting of a rate of taper, and for the tool to follow that rate of taper with high precision.
It is not intended for contour turning, as one might want for turning barrels.
"is that just the tail stock? or something else"
It is an attachment which is installed at the time of manufacture and which allows for setting the rate of taper to tight tolerances.
For relatively short, relatively steep tapers, the compound is used in preference to the taper attachment.
For relatively moderate length, relatively moderate tapers, the taper attachment is used.
For relatively long length tapers a "variator" attachment is available for some Monarch lathes, but not for the 10EE.