Hi Tracie1212,
to answer your question quickly: yes, I do adjust my Tresiba dose regularly, otherwise I have lows like crazy… Of course I let my endo know; however that kind of decision is up to me (have been T1 for 30 years and my endo trusts me).
As for half doses: could you perhaps try and inject one unit less on alternate days? E.g.: if you normally inject 8 doses, you could choose to inject 8 on Monday and 7 on Tuesday, then 8 again on Wednesday and so on. I hear it is often done to substitute for half doses.
As for injection site, my endo advised me to use the upper part of the body for Tresiba (however I always choose the upper body for any kind of insulin: found it works better on me). But no special reason given.
I hope you will be feeling better soon, let us know!
A hug!