I guess a information on safe periods would help you in this regards.
From the day of the start of the periods till the next 7 days, the chances of getting pregnant are very very less. Say about 5 percent chances only. But the next about 10 days are the most fertile days of the period in which the chances of getting pregnant are about 80 percent.
And then about 5-7 days before the onset of the period are again infertile days.
These figures are just rough figures just to make you understand.
I think the first part of your question is answered.
Now coming to the second part, I would say instead of the penis going deep, the sperms when ejaculated should go a bit deep to increase the chances of your pregnancy.
All the best.