The word mere is neither wrong nor useful in that particular construction. Completely different wording might use 'mere' to make much of the difference.
Since you ask 'do these sentences make sense?' they do, but not readily
Centuries do not have advents. They have, for instance, starts.
Mere data is hardly relevant; information is worth sharing.
Ability is singular.
‘With the advent of… anything… anything has been unprecedented’ more than overeggs the pudding; it tries to give one sentence two subjects.
If the subject is the 21st century (or its advent) then we might have acquired an unprecedented ability.
If the subject is our unprecedented ability, then that might have become apparent in the C21.
The (whatever) of the 21st century is contradicted by any advancements in recent history. To maintain the C21 theme, speak at worst of recent ’years.’
If the idea is to highlight the potential, the deluge of information and the scientific advancements should be the other way round.
If the idea is to highlight the fact that our ability to collect and share copious amounts of information provides the potential for anything, the deluge of information and the scientific advancements should be the other way round.
We might, for instance, develop from the abstract or extrapolate either way but we model from the practical to the abstract.
Applications either help in our daily lives or aid our daily lives.
If you're trying to convey that practical applications are now viable then start with those words: 'Practical applications are now viable'. That might mean slipping sideways to something like 'Practical applications previously undreamed of are becoming viable…'
I see that's not an ideal choice of words and the fact is, you's said about eight different things before introducing your main point, when you could easily have introduced it at Word One.