Hi Barbara Louise, like you I've been on thyroid replacement for nearly 30 years & latterly on HRT. Although it's documented that transdermal oestrogen is less likely than oral to affect our thyroid levels, a number of us on this forum have found we have had to tweak our thyroid dose in response to transdermal HRT.
Wrt to your 2nd question, if your thyroid levels are not optimal for you, your body may struggle to utilise your HRT as well as it might, meaning symptom relief could be compromised.
If your GP is not receptive to the possibility your feeling unwell could relate to a thyroid-HRT interaction & you sense it is, then as CLKD suggests you may have to ask to see an endocrinologist, though another option first is perhaps to try a different GP. Your FT4 is certainly on the low side according to the ref range for the lab I use, though your TSH looks OK-ish, but of course may not be optimal for you. I take it they don't test your FT3?
We have a thread called Thyroid Issues & Support you may like to have a look at some time.
Wx