“With time” and “over time” can by synonymous, they though would not always be used interchangeably.
1. “With time, those wounds will heal.” – means that as time advances, the wounds will heal. Here you can equally say “over time.”
2. “The changes over time in this experiment are not what we expected.” – while the changes did take place as time advanced, in this context ‘over time’ gives more of the sense of a period of time, or a specific relation of something to time. Here, to me, ‘with time’ would not fit well.
“Overtime,” as one word, can be a noun or an adverb and can mean “time in additional to what is normal” – and may be used, for example, in sports or in work contexts. “There was no overtime for employees this month.” (noun); “They worked/played overtime.” (adverb)
Hope this helps!