There are many factors that can prevent a slave from joining the combat group. The primary difference between the starting slave and a random slave will be that the sum of obedience and loyalty will be lower.
You haven't stated what two portals you have, so I'm not going to guess the other two. If you go outside the mansion there is a map button in the top right corner of the screen. There are 4 major cities on the map; 3 of your portals will go to these and the fourth is a secret until you complete more of the story line.
The starting slave events have no impact at all on the beauty of the slave. If she grew a tail, then that is because you had her use multiple potions, which each raise magic toxicity. When a slave's magic toxicity is high enough, then they will sometimes mutate randomly at the end of each day. The only way to reduce the toxicity is to wait for it to gradually decrease each day or have a mutation occur. Two possible mutations are growing a tail and being randomly assigned a new beauty value. The tail can be removed in the lab, but the beauty cannot be easily fixed to any significant amount. The lab operation to increase beauty will only make a minor improvement. You could try to mutate her again to get a beauty as high as 90, but your chances of success are very, very low.
Both of those items drop from Ooze monsters after combat, and both can be produced by sex with rare races of slaves.
If all you had were low level characters then it may not matter much who you assign, but each job specifies the stats that impact the results of that job. A better qualified lab assistant will result in cheaper operations with lower recovery times. A better chef will result in spending less food to feed each person every day.
