Both the infertility and cancer issues are myths. Here's some real medical opinion on both. The second source (7 Myths) also mentions the issues of fertility and quick development.
Fertility Is it true? Do COVID-19 vaccines cause infertility? | Australian Government Department of Health
Do COVID-19 vaccines cause infertility?
There is no scientific evidence to support this. None of the
COVID-19 vaccines currently under review by the
Therapeutic Goods Administration (TGA) cause sterilisation/infertility.
The TGA will not approve a vaccine for use in Australia unless it is
safe and effective. This includes impacts on fertility.
The theory that COVID-19 vaccines cause infertility is based on the disproven idea that one of the spike proteins in COVID-19 and the Syncytin-1 protein (which help placenta development) are the same. They are not.
The COVID-19 vaccine, like other vaccines, works by training our bodies to develop antibodies to fight against the virus that causes COVID-19, to prevent future illness.
There is currently no evidence that antibodies formed from COVID-19 vaccination cause any problems with pregnancy, including the development of the placenta.
In addition, there is no evidence suggesting that fertility problems are a side effect of ANY vaccine.
People who are trying to become pregnant now or who plan to try in the future may receive the COVID-19 vaccine when it becomes available to them.
Cancer Fact Check: 7 Persistent Myths about COVID-19 Vaccines | Memorial Sloan Kettering Cancer Center (mskcc.org)
Myth: The mRNA vaccines change your DNA and could cause cancer.
Truth: None of the vaccines interact with or alter your DNA in any way, and therefore cannot cause cancer.
Messenger RNA (mRNA) is not the same as DNA and cannot be combined with DNA to change your genetic code. Here’s now mRNA vaccines actually work:
The mRNA vaccines use a tiny piece of the coronavirus’ genetic code to teach your immune system how to make a protein that will trigger an immune response if you get infected. The mRNA is fragile, so after it delivers the instructions to your cells, it breaks down and disappears from the body (in about 72 hours). The mRNA never even goes into the nucleus of the cell — the part that contains your DNA.
Therefore, there is no truth to the myth that somehow the mRNA vaccine could inactivate the genes that suppress tumors.