No you don't need symptoms to actually be pregnant. It's a common misconception that if you don't have symptoms you're not pregnant or the pregnancy is not viable. In regards to your other question, no you also cannot have a true menstrual cycle. Ovulation is what triggers a period and this (in almost all women) is impossible while pregnant. During a period you shed the lining that would be used to support a growing child. If this happens while pregnant you miscarry. It IS possible on the other hand the experiance vaginal bleeding which is very different and possible while pregnant. This can at times also mimic a proper period.
Full and sore breats may not happen in pregnancy especially in early pregnancy however if you have your period it really isn't possible to still be pregnant bc shedding your uterine lining makes it so baby cannot stick to the uterine wall