Most women ovulate 14 days BEFORE their period, actually. So no, 3-4 days (a "few") before her period she should not be fertile.
The chances of becoming pregnant from the precum are much higher than the chances of her touching sperm and then her own vagina; don't even worry about that!!
Please, use a condom every time, and never put a naked penis inside a vagina - unless you WANT babies! In other words, don't go "bare" initially and then put on a condom: wear the condom the WHOLE time.