1&2) That depends on the level of Sector-Sight Obscuration given to the comp/facilty that is cloaking the HWs. If it is level 3 cloaking, then yes, you can detect it eventually. If not, blow up the star in their home system, and that will get rid of them.
3) Yes. Technically, it wouldn't be the standard game, but a special mod. You'd have to find all Monster techs, comps, ships, facilities, etc. in the DNM data files and copy them into another mod (or a copy of the normal game). I do not know how much work it would take to get the monster AI files to work with the normal tech tree (or a modded one).