Yes, my friend also had thyroid cancer, had her thyroid gland removed and did the radioiodine treatments. She just had a healthy baby boy. As long as you are on the correct dose of thyroid replacement hormone, it should not affect your ability to get pregnant.
Yes, it's possible to get pregnant without a working thyroid. I did it, and I'm trying again. Though my thyroid just stopped working, rather than surgically removed.
If trying to get pregnant your numbers should be optimal. Ie. TSH should be in the range of 1 - 2, and FT3 and FT4 (which are more important that TSH) should be at least middle of the reference range, or a bit higher.
When you get pregnant you need to tests levels monthly and adjust your thyroid meds. It is normal to need more thyroid meds during pregnancy. Usually an increase is needed as soon as you know you're pregnant.