Psoriasis does not affect fertility or rates of miscarriage, birth defects, or premature birth.
During pregnancy there can be an improvement of psoriasis, especially in the late first and second trimester.
There are smaller chances for exacerbation or worsening of psoriasis during pregnancy.
If only one partner if affected with psoriasis the chances for psoriasis to be passed on to baby is 28%, and if both parents have it, the chances for inheriting are 65%.
Psoriasis treatment isn't recommended during pregnancy, and in order to minimize the frequency of its flare ups, therapy is taken before conception (there must be a period free of drugs before even trying to conceive).
Thyroiditsis can be passed to your baby, but, that happens rarely.
It is expected for patient with treated Hashimoto's not to have problems with conceiving and pregnancy.
It is important to consult your endocrinologist if you have to take increased doses of thyroxine during pregnancy.

Best wishes!