The tenor here is that it's normal. In my experience, the tail may get looser with age but I have had several bitches whose tails drooped like this like this and it was because they did feel unwell in some way. I would still get the vet to give her an 'MOT' (a thorough health check) before jumping to conclusions.
@debradownsouth Thank you - just another example of rumours being magnified! Personally I believe nothing unless I hear/read it from its source. I know it can be aggravating to be doubted and I apologise if anybody finds it upsetting. I just imbibed 'go to the horse's mouth' from my parents.
You know that you've made a mistake in giving them treats at an early stage of their introduction so now you know to do this in a different way. Just be patient and go back one space! When they are separated (when she has her op) again be wary when they are reunited. From now on I would feed treats or their meals side by side but in separate crates so that there is no chance of fighting. I don't think the fact that your male got the worst of the fight will be taken as a lesson by him, so be continue to be vigilant. Have you asked the breeder's advice too? She/he will have experience of the bitches temperament.
You've been given very good advice but some is just not as good. NEVER be aggressive to your Basenji - it'll have the opposite effect and make her really aggressive. Basenjis never forget! Positive training can be more difficult with an older puppy but perseverance and consistency is the key. In my opinion a Basenji isn't naturally an aggressive dog, this has mainly come about by incorrect handling in the early days by ignorance of the breed. A puppy that leaves it's breeder is often 'spoiled' by the owner who doesn't take much notice of advice given by that breeder on socialisation, correction etc. I can't find evidence that you've consulted the breeder on Lily's current behaviour. Apologies if I am mistaken and I'm not criticising you in any way. You've obviously tried so hard with her. So pleased that you've joined this forum where you'll find advice from many experienced Basenji breeders who give excellent advice and help. I'm sure you'll find that you'll have great success. The other matter of them eating their own poo can mean that she is deficient in some of her nutrirional needs so check this before trying other methods. Eating other animal's poo is quite common and actually, I've never been able to stop this except that some later do. I have sheep with mine and have had little success in stopping my Basenjis eating their poo. I find that some never do it and some keep on until old age! My current remaining dog rarely does this. I wish you the very best for your happy future with Lily. She's lovely.
Personally, I don't believe that being alone is any more difficult than having another puppy. After all, there's always a chance that he doesn't get on with the new one (little or adult). I totally agree that he'll benefit from having more attention and bonding with you. There's plenty of time later to think about having more Basenji company.