Is it safe to use cleaning products during pregnancy?

No. You are safe with castille soap and diluted hydrogen peroxide. Citrus peel based cleansers are okay as well. Use nothing with chemicals in it you can't pronounce.
Yes. Generally yes, cleaning products are fine. Probably avoid strong acids or bleaches. Make sure your area is well ventilated. If the odor is very strong or makes you feel ill or nauseous you should probably delegate. Of course, read your labels.