Your frog will probably survive okay with the filter but whether the noise and vibration are desirable is really a matter for personal judgement. Filters containing a motorised pump are designed principally for use in fish aquaria and most fish originate from rivers and streams with strong water currents. Xenopus frogs, however, originate from pools where the water's still or very slow-moving. You say that the noise annoys you, which I can understand and which, together with your concern for the frog's welfare, suggests that it would probably be a good idea to consider using a less powerful filter.

Solitary females do sometimes expel eggs. In my experience it always happened in spring time (around April) when hours of daylight started getting longer and air temperatures a little warmer, which is in tune with the seasonal influences of the climate from which these frogs originate. Egg production is usually an indicator of good health and nothing to be concerned about.