Simple question on high bandwidth Opamp reproducing low frequency signals
In general, using a 'faster' opamp than you need is absolutely fine. An ideal opamp will have as close to flat gain as possible across its entire range; see the graphs in the datasheet if you're uncertain.

However, faster opamps tend to be trickier to use; they're more likely to oscillate, so you need to take care to roll off the gain to prevent that; they'll require more attention and care paid to proper power supply bypassing. Some high speed opamps are not unity gain stable, so you need to be certain you're operating at a gain that they're stable at.

Faster opamps may also make tradeoffs to achieve that speed; for instance, current feedback opamps have a low input impedance on the inverting terminal, so you can't easily use them as differential amplifiers, and need to account for the input impedance when calculating your feedback values.